My laugh sounds so evil.
Hi Guys, it's Pierce from Pierce'sWorld.
And today we are going to do the Paw Patrol Easter Mini Figures!
You can see the golden Chickaletta.
It's the rare one I want to really get.
You see it says," Fine the Golen Chickaletta!"
So, this is the full set of 30 Easter eggs!
I love opening surprise eggs.
And if you want to see my other surprise videos, please click the 'i'.
Yes, the 'i'.
You can only buy these at Walmart.
And Paw Patrol is from Nickelodeon.
These are the characters we are trying to get.
So, you want to try to collect all 6 pups.
This is Chase, Zuma, Rubble, Sky, Rocky, and Marshall!
And if you're new to this channel, please hit that subscribe button right there. Yes, right there.
So, you don't miss any of my upcoming videos.
Let's start opening.
There's a swinging egg in this party...
I love to do this with my surprise eggs.
I caught the egg...
It has the Paw Patrol logo right here.
It's the Paw print.
Like this...
Do the Paw Print! Uh-huh!
Let's see who we got.
Finally!
It took me like a while!
And I knew we were gonna get Rubble because I actually peeked, and saw his little tail... and I was like...
Uh-huh we got Rubble.
Rubble is a construction bulldog.
He's strong and eager to help.
And he's also funny. He likes to skateboard, snowboard, and get covered in mud.
Let's keep going!
Oh, this one is yellow and purple.
This is how I always open things.
Duplicate!
1, 2, 3... let's do it!
Oh yeah!
Yes!
New Pup!
Finally! Who do you think we got?
Do you have a guess?
Who looks grey? Who looks green and white? Rocky does!
If you guessed Rocky, then you are right.
Oh, he is lifting his paw up.
Standing and he is lifting his paw up.
Rocky is a 6 year old mutt.
And he is a recycling pup, and he is very creative and has thousands of ideas.
And someone else's trash is his treasure.
And I think we figured it out because this is all Rubble.
This is all one other pup.
We are not sure...
We are just guessing.
I think we got Zuma. Yeah, it's Zuma.
Now, there's Zuma.
He loves to get wet. He's a water pup.
Zuma is a labrador pup.
And at 5 years old, he's the youngest Paw Patrol member.
He always likes to laugh and surf.
We got Sky!
And here is Sky, and she is a flying pup!
She's 7 years old, and she's a cute cockapoo.
She's older than me!
I'm 6, and she's 7!
Do you know what a cockapoo is?
It's a dog that's half cocker spaniel and half poodle.
Her favorite videogame is Pup Pup Boogie.
Marshall! The fire pup!
I just have 4, and I just need Chase.
Ok, here is Marshall.
So, Marshall is the team's brave fire dog.
And he's a 6 year old Dalmatian puppy.
Did you guys notice that we didn't open that many eggs?
But, we got a lot of characters!
So, you know what we noticed?
To save some money and you want to get the whole collection, buy the eggs in a row like this... up or you can down.
It changes on every single row, because every single row has a different pup.
But if you buy it like this way (horizontal), it will all be the same.
You get a matching one. Does that make sense?
Makes sense to me.
If our guess is right, then I think we got Chase.
Chase it is!
And here is Chase!
So, Chase is a German Shepherd police pup.
And he's 7 years old.
And he's a natural leader.
And he can sniff anything out, but he is allergic to cat fur and feathers.
So, now we just have to guess which one egg has the golden chickaletta.
Chickaletta is Mayor Goodway's chicken.
So, wish me luck!
Wish me luck!
Hopefully, there is a golden chickaletta, and we don't have to open everything.
I think we are going to try for this pink one.
We never go for pink.
I took a peek, and this one is Rocky. Agh!
It's really annoying.
This one is Rubble...
Agh!
Please tell me I get the golden chickaletta.
I'm begging for the golden chickaletta right now.
Try purple. We never did purple.
Chickaletta!
Golden Chickaletta!
It's Zuma.
AGh!
Man! This is still not going well!
This is like a guessing game.
Seriously? It's probably Chase or Zuma.
This is not a great day!
Man, let's start opening!
oh my goodness!
Yes! Finally!
The golden chickaletta!
Look!
The golden chickaletta!
I'm so happy I got the golden chickaletta!
So, this is the complete collection of the Paw Patrol Easter Eggs.
I'm so happy I got the golden chickaletta.
Now, guys, remember, if you want a shout out, subscribe, like, and comment as often as possible for a chance to be picked.
Stay tuned for our 5,000 Subscriber Giveaway!
So, if you liked this video, please give me a big, big, big thumbs up!
And don't forget to subscribe to my channel, Pierce'sWorld.
Follow me on Facebook and Instagram, and check out my Pinterest page.
Ok, I'll see you guys next time.
Bye!
For more infomation >> PAW PATROL Surprise Eggs Easter BLIND BAGS Opening GOLDEN Chickaletta - Duration: 9:31.-------------------------------------------
RCMP Officer for the Day - Runner up - Duration: 1:03.
I would like to be an RCMP officer for a day because…
Police are so awesome because they have my favourite protection like chest armor,
tazer, bullets, ak-47s, mini guns, cars, trucks,
helicopters, bikes and shotguns.
Cops have shepherds as dogs.
Police have daggers.
I love to hunt but not big animals
only birds with a bow.
Why do people hunt big animals?
Why do you have guns?
I want to be a swat officer some day.
Who is your chief?
I want to make my own police academy one day
and I want my friends to be officers and I will be chief.
I will drive a cop car and my friends will be swat officers
and they will drive a black swat officer truck.
I love working and helping people.
Helping is the best thing that I love most and working is good for everyone.
I love Royal Canadian Mounted Police.
Sincerely, Future Officer Mackenzie
-------------------------------------------
Jon Hamm and Jack McBrayer Leak All Their Secrets (Before The Government Can Sell Them) - Duration: 2:52.
- Hey, everyone!
Extremely likable and non-threatening celebrity
Jack McBrayer here.
- Extremely likable?
- Jon Hamm here
to help me out. - Hi, everybody.
- Now we all know that the government is now able
to monitor us by hacking into our phones
and TVs and computers.
So, I thought I'd take this opportunity
to just leak all my compromising info myself
before they can use it against me.
Ready?
- I'm very nervous.
- Don't be.
- Okay. - You know, I mean--
- Okay, well let's see where this goes.
- Sure! Okay.
A lot of celebrities lie about their age.
I'm no different.
- True.
- I tell people I'm 43 years old,
but in reality,
I'm a mannequin who came to life but ten years ago.
- In fact, I animated him.
A lot of people don't know this about me.
I'm a wonderful woodworker named Geppetto.
- For the longest time,
I thought the term preemie was short for premium baby,
so I would go around congratulating pregnant ladies
and say, "Oooh, I hope it's a preemie!"
- That's actually true.
- [Jack] Well, that's what
I thought. - I was born a preemie,
and this is what happened.
Premium.
I don't wanna give too much up,
but if we are sharing.
- Okay.
- I will tell you that Jack's genitals
are in fact made of actual junk.
- Found objects, really.
- Yeah, there's a lot of rebar,
some busted concrete bits,
an old soup can,
and a cartoony fish bone.
Oooh, tell 'em about your teeth.
- Yes.
- Actual Chiclets.
He can't really chew anything harder
than a boiled banana because the teeth will just--
- Just turn into
like mushy gum. - Actual chewing gum.
Chewing gum. - Yeah.
- The one thing I will say about Jack,
delightful breath.
Mostly it smells like bananas and chewing gum.
Most people know me from Mad Men.
Most people know you from?
- 30 Rock?
I auditioned for Mad Men.
- [Jon] What part?
- Peggy Olson.
(laughs)
- How did you get your job on 30 Rock?
- I got 30 Rock
because I have a Polaroid of Lorne Michaels
strangling some other Canadian by the river.
- And that's why we need the ACLU.
So, thanks ACLU.
We really, really love what you do
and the inspiration you give us.
- My hair is spun sugar.
(big band music)
-------------------------------------------
The War for Iokath: The Republic Mobilizes - Duration: 0:27.
You compiled a report on the Alliance Commander...
What's your recommendation?
He's a hardened veteran with extensive personnel and resources.
Even with our numbers, I doubt our chances in a head-to-head battle.
Asymmetrical tactics would be best...
A surprise attack. Surgical and precise.
Then we'd better shock the Alliance Commander.
Gather your top engineers and rally the troops. I'm coming to Iokath.
-------------------------------------------
Surgeon Simulator TWO FOR ONE BRAIN + EYES Transplant Funny Moments - Duration: 6:33.
hey welcome back now I know I know you
might be like heart kidney does are
pretty close but brain transplants I
don't think so well you know after
christmas new years my wife leaving me
with a new boyfriend and taking all my
money I am several levels beyond
financially but so I gotta work the ex
route you gotta do what you gotta do am
i right but on the other hand Bob here
what Fergus has read transplants in like
two weeks and I mean every time the
nurse was coming to my office and be
like oh my god dr. we have an emergency
transplant the patient in science and
I'm like is it Bob again she's like yeah
you think that after all the times I
saved his life I mean granted I did kill
him much more than that but after all
that you think he'd give me a tip or
something at least but no more progress
richest part and also an ungrateful
prick you know Bob is the new year so no
organ failures how about that for a new
year's resolution all right okay just
broke your skull in the pieces I don't
know if he's actually going to be able
to use that again please stop we're
going you're making this much harder bro
ok now let's stop the bleeding right in
the eye that is good and now give me
that stupid rotten brain of yours oh my
god i broke my ending got up oh no never
mind it's fine now give me that rotten
breath all right dad Gus in but at least
it's out let me just get you a new on
can he work with two brains I mean
that'd be pretty cool just don't drop it
yep it is sideways but think it's gonna
work no I can't put two brains I got
damn it good don't stop I mean you don't
even need it doesn't matter and let's
just cut that come on there we go if
you're going to fix itself because I do
not want to touch it it looks very very
sensitive come on well guess i'm going
to have to and i broke my finger now
okay oh he's alive that was pretty fun
but you know what since its new years
and all
we're going to do two operations in this
episode perform an eye transplant whoa
that is going to be interesting okay
what the hell why does he have goggles
if I want to take off its breaking on
just give me the goggles no not the
respirator the goggles no way do I
really have to break him off oh my i am
going to end up snapping his neck whoa
what the hell please don't tell me that
was here all the time and my demise
doesn't see it god damn it can I use
this to cut up the goggles please I mean
it's going to hurt but okay that is
right on his face all right goggles are
off ladies and gentlemen now on to the
eye okay what the hell do I do now hey
pup you want blue ones or the brown one
i think i'm going to give you both
you're going to look pretty like that Oh
what is this is this something I have to
use no way do I gotta do that to take
his eyes off well I guess take a bite
your eyebrows Bob oh my God look at that
you look beautiful like freaking hit man
can I use stencils to get it out I mean
I am clueless here might as well try
everything okay a pen will do know that
does not freaking work neither does the
laser cut it is only killing you look
had that blood going down bro all right
you know what the drill is the only
viable option left here so might as well
go for it Oh does not seem to be working
so you know what what I'm going to do is
go back to my medical books okay the
internet and see why I gotta do I'll be
back in a sec I am back from consulting
my magical books I have figured it out
but let me tell you it is not pretty
okay first off let me just punch the
shit out of them to take the goggles off
come on give them to me Bob given to me
they don't even look good on you okay
so that way and okay he is bleeding but
that is fine good you're gonna bleed
even more trust me and now to the
disgusting part yep there it is you have
to wedge it deep in there and fucking
pull it out that's how fucked up it is I
am so sorry did there we go that is the
second one oh my god this is fucking
awesome yeah shit come on there we go
okay next up we have to bash him in the
head with this box this little girl dude
just let it okay now you know o clock
and help that is gross that is so gross
please don't make it any grosser stop
moving thank you okay that is one out
okay quietly dude who it is over hold on
let me just stop the bleeding real quick
none and then I need to sign it no don't
okay you know what fuck the bleeding we
aren't doing this without it you mean
those freaking eyes did okay I got one
okay there we go you finally grabbed it
just oh god this is hard this is going
to be a close one come on no just just
get in there get get are you in okay I
thank you it and let me just get another
one
Bob only make you unique I want to make
you stand out ugly but still unique i'm
going to give you this read you please
just lift your fucking head up and not
all okay he almost bled out well we're
going to see what laughter does that I'm
not going to be able to unsee this
operation hi my name is ray I meant this
piece of shit also made this other piece
of shit and if you two hate lizards and
subscribe to this channel because fuck
them okay bye boo boos
-------------------------------------------
Volley Heart! FOREVER「AMV」 Anime Pictures [haikyuu!!] - Duration: 2:15.
Once in the field, the ranking does not count!
Next time for sure we will win! the next!
Well, you have nothing to fear!
Continue to look in front of you, because behind you there is me
Win! you have to win!
Nishinoya!
kageyama
Give it to me!
It is feared more the better ..
more he will shine
the wall will focus on him.
I wait for you!
freed the way to our ace!
Numer then!
amagazine..
I feel excited!
* I can not take it *
One more!
Nishinoya nice ball
Again, again and again!
Stay focused and do not stop running!
Again!
one more time!
how did it go? did you have fun? Tadashi!
No!
I want my body to move as I say.
control the ball.
fight with stronger opponents!
We have no time!
Stop it now..
it's impossible!
Mister, continues to train ..
Please!
the wall jumps ahead of you ..
see the network closely and ..
Hit!
-------------------------------------------
Facing Acne 2017 Scholarship Submission - "Helping our Health" - Duration: 4:38.
It's a fast new world of the World Wide Web
Ain't it funny how info spreads
So easy, it's peasy, when our pores are greasy
We can hop online like lemon squeezy
The internet is a tool you see
To help us get fit, to help us feel free
In our everyday lives and our familes
Access to thousands of resources with ease
What's up with this dead skin and stuff?
Am I soaping too hard? Do I drink enough?
How much water, fitness, pills, or citrus
am I gonna need just to feel like me?
With one search in Google it's easy to see
Check out Mayo Clinic or WebMD
For symptoms, for myself, and my family
I can find out what foods that I need to eat
I can access info for my own safety
For medicine, the exact dose that I need
It's important to be sure so you don't OD
And best of all
IT'S COMPLETELY FREE!
It can be a pain when you're going to college
Most of the time, it's the 'rents with the knowledge
Of immunizations,
vaccinations
Sometimes it's easy to lose your patience
But the web is makin' it better than ever
You can simply log in to your health provider
While you're sitting at home doing whatever
View and print out your records for a new semester
With clicks of a button you can get opinions
Schedule an appointment or make decisions
Regarding your personal wellness and visions
Yes, the power of the web helps you go the distance
10 pound, 20 pound, 30 pound weights
Jump-ropes, yoga mats, bikes and skates
Blenders to help us make them protein shakes
Books, music, and art that motivates
We can add to the bag, to the basket or cart
With a click of a mouse we can make those smart
Decisions-- products that are good for our heart
It's honestly not at all hard to start
And if you're like me and trying to save money
There are still ways left to hit the ground running
WikiHow, YouTube, bloggers, Instagrammers-- it's stunning
Knowledge is everywhere if you just do some huntin'
The web is a powerful tool you see
To help us get fit, to help us feel free
In our everyday lives and our families
It's all out there to access with ease
When you're feeling down or you're feeling blue
There's lots on the World Wide Web to do
Like videos of kittens, puppies or cats
Shows-- the Office, and Orange is the New Black
Music, podcasts, Netflix and Facebook
But don't get caught up on how "great" your friends' lives look
Boost your self-confidence, blog, read the news
Search ways to beat stress, however you choose
Those Amazon buttons that are sweeping the nation?
Maybe we'll have them for our medications
A doctor will approve and fill our prescription
With the press of a button we can get a subscription
To meds by mail--or delivered by drone--
Well, that would avoid awkward talks on the phone
Yes-- and instant messages with expert physicians
Could help help us out in the worse positions
If we're stuck at home or aren't physically able
We could DM doctors from our kitchen tables
And we could stay connected from our phone or tablet
Track progress with workout buddies with applets
Or applications to beat our personal best
To put our skills or motivation to the test
To lose weight, to gain friends, to help us get stronger
To help us sweat and live a little bit longer
Fitocracy, Extra Pound, Daily Mile
Apps working to bring people together in style
Social media platforms for getting fit
Could be the future of healthy kids!
Let's face it, what it takes is the help of the village
Determination, positivity, courage
United we could change ourselves for the better
Because there's nothing like getting healthy together
It can help us
get easy, fast, professional help!
It can help us
be informed!
It can help us
make the crucial paperwork easier!
It can help us
eat smarter!
It can help us
purchase healthy goods!
It can help us
inspire us in our health!
It can help us
take care of our mental health!
It can help us
embrace our best self!
The web is a powerful tool you see
To help us get fit, to help us feel free
To help us feel strong and know inner beauty
'Cuz that's how it always was supposed to be
We should be chasing, embracing, relentlessly racing
The up and up that the wide web is facing
To help us continue at our own pacing
'Cuz liberating ourselves and our health
...is amazing.
Hi, I'm Stephanie behind Stephanie Scribbles
And thank you for watching my video submission for the Facing Acne Scholarship!
As you can see I'm facing a little bit of acne myself right now,
But this video was so fun to make, and I hope you guys had as much fun watching it
As I did filming/drawing it.
So if you guys have any tips or ideas or the ways you use the internet
to impact your health in a positive way
let me know in the comments below and thank you for watching!
-------------------------------------------
IT OFFICIAL TEASER TRAILER REACTION AND REVIEW - Duration: 4:12.
whats good YouTube its Casper, miss P here
and today we back to react react to" IT"
official teaser trailer let's get it
you
oh damn each other notable so that's all
I ask is this a shit it's stephen king
yellow jeans
oh you saw her out it was too clean oh
thank you I think so Oh yo that thinking
hello fasten mm-hmm this gonna be better
than yeah and I saw the original what I
love about that and that one was good I
didn't see the original into like last
year something wait worry I don't know
how we started was gonna be a boring
movie I was mixing that up with the with
the John Wayne Gacy story and that was
about that guy who dressed up yeah that
looks something like that yeah i was
always mixing because i remember my
parents watching the that John Wayne
Gacy movie when I was little and then
everybody was like yo you ever saw that
movie with the clown and always thought
it was that movie right then I'll catch
a key it was like my first scary movie I
gotta sleep for days tel Aviv fishes
have fun watching you cum nothing well
that was it trailer teaser trailer damn
it doesn't teaser for two minutes and 33
seconds it was doing awesome I can't
wait for the trail of one that's just a
Jesus yeah yes notice that the kids the
group of friends are more than the
original movie the original was really
like three or four friends over here is
like a good do you think 36a nagar them
because later on dependent meeting other
a bikini well okay and they didn't show
that beginning the boy what he had
disappeared yeah let me know I was not
coming that was it let me know what you
guys thought about it like comment
subscribe all of that
-------------------------------------------
Pakistani Atheist Tayyab Sardar Apologizes For His Blasphemies Embraces Islam FunKarachi com - Duration: 4:02.
Please Subscribe My Channel
-------------------------------------------
The number e explained in depth for (smart) dummies - Duration: 18:38.
Welcome to another Mathologer video.
A while ago I did this video in which i
wanted to explain the mysterious
identity e to the i pi is equal to
minus 1 to Homer Simpson who encountered
it in one of the Treehouse of Horror
episodes. So my mission was to explain
why this identity is true to someone who
knows only basic arithmetic: plus, minus, times, divided
Today I'd like to do the same
for the other fundamental facts about
the number e. These fundamental facts
I'm thinking of include this truly
amazing identity here that expresses the
exponential function as an infinite sum.
I'll first show Homer and you how you can
derive this identity from scratch just
using basic arithmetic. Then we can set x
equal to 1 and use the resulting sum to
calculate an arbitrary number of digits
of e. Now here the main point is to
figure out when you can stop adding the
terms of this infinite sum and be
absolutely sure that you've calculated
the first, say 1 million digits of e or
however many digits you are after.
Then i'll show you that e is an
irrational number, why e cannot be
written as a fraction. And for the finale
I have to catch Homer on one of those
days that he's super smart, that he knows
a little bit of calculus for example. The
finale is about showing why the
exponential function is its own
derivative, some super famous facts about
the natural logarithm, the inverse of the
exponential function and a couple of
other super cool insights to round
things off. Now the main point of
the video is to show you WHY all these
things are true and not just talk about
them like it's usually done on YouTube
and to show this to you in as elementary
and accessible way as possible.
As usual please let me know in the comments
how I did in this respect. In the e to
the I pi video I first showed Homer that
if he invests one dollar at an interest
rate of one hundred percent and
compounds the interest N times during
one year he'll have that many dollars at
the end of the year. For example, if you
compound twice you end up with two
dollars and twenty-five cents. Now the
more often you compound the interest,
that is, the larger the N, the more money
you'll have by the end of the year. But
this amount does not grow forever.
There's a limiting value and this
limiting value is the number e which is
approximately 2.718. Then I show Homer
that this actually extends in a
straightforward way to the exponential
function. So plug in any value for x like
for example 5, crank up the N and in the
limit you get exactly e to the power
of 5. Then we just go for it and plug in
i pi for x and see what happens when we
crank up N. Translating all this into
geometry leads to this neat complex
number pokeball there. It looks like a
pokeball right? The green point shows what
complex number we are dealing with for N=6
Then cranking up N you
can see the green point tending towards
-1 and so e to the i pi is equal to
minus 1. Super neat, check it out. For
today I'll return to this point of the
argument here and branch off. Now
let's try something super natural. I think
anybody would try this. Let's expand the
right side for a couple of small N and
see whether we can see some sort of
pattern. So N equals 1, nothing to
expand here. N equal to 2, I'm sure
everybody watching can do this. N equal
to 3 and equal to 4, and so on. A couple
of patterns are emerging, right? In terms
of green and blue bits it's clear how
this continues. What about those other
numbers? Well, there's also a pattern and
I'm sure many of you will be familiar
with it from school. These are binomial
coefficients and can be written like
this. We've got our pattern right there.
But before we carry on just a reminder
that there is a special way to write and refer to the
denominators 1, 1 x 2, 1 x 2 x 3, and so on.
For example, 1 x 2 x 3 is written three exclamation mark
and it's called 3 factorial. And there we
have 1 and 2 factorial. Now that we've
established a pattern let's crank up the
N and replace 4 by something big, say
1000. All right, so here we go. Now what I
want to do is swap things like that. And
what I mean by this is I want to swap 1!
by 1000, 2! by a
thousand squared and 3! by a
thousand cubed. And so on so let's just
do it. Now let's have a look at the
fractions. Okay this guy here is equal to
1. That one is equal to 1 too. What about
that one here? Well it's close to 1 and
as we replace 1000 by larger and larger
values this fraction will tend to 1. All the
other fractions that you see here also
go to 1 and so all the numbers here will
go to 1. And so in the limit we get
this identity here. And if you are a
mathematician you can dot all the i's and
cross all the t's to prove that this
amazing identity is really always true
No matter what you plug in here for X. If
you know more maths you may have seen
this identity before but derived in a
very different way and in a more general
context. In that general context it's
called the Maclaurin series of the
exponential function and there it is
derived using calculus. Setting X
equal to 1 we get this identity here and
it allows us to approximate e by adding
more and more of those simple terms. Now,
as promised, and i hope Hormer is still with
us, there's only basic arithmetic and
some glossing over details involved.
Before we calculated e by cranking up
the N in this expression here. In
terms of using this expression to
actually calculate a good approximation
for e the problem is that every time we
up the N we have to start afresh and
discard everything that we've
done so far. More importantly, although we
know that we get e in the limit, to start
with we have no idea how large an N we
have to choose to be able to guarantee
that we found correct to the desired
number of digits. On the other hand, the
infinite sum is much much more
user-friendly in this respect. As we add
more and more of those simple terms our
approximation gets better and better and
it's also very easy to estimate how well
an approximation a chopped-off partial
sum is. So here if top of the infinite
sum at the 8th term. How close does this
get us to e? Well, the error or the
difference between e and this
approximation is just the sum of the
remaining terms. Let's estimate how large
this error is. the 8! at the
bottom is just 1 x 2 x and so on to 7
which is 7! times 8.
9! is 7! times 8 times 9,
and so on. Let's pull out the 1/7!
Now the bracket is still very
complicated so let's do something
drastic, let's replace the 8, 9, 10, etc.
in the denominators by 2s. This
gives the new simpler expression. Is this
new simpler expression greater or
smaller than the error? Well we're going
down in all the yellow denominators, so
that means that the new expression has
to be greater, right? But now it's really
easy to see that in the brackets we have
1/2 plus 1/4 plus 1/8, and so
on which you all know is equal to 1.
And so to summarize, the error we
make by chopping the sum off at the
1/N! th term is equal to 1/N!
which is very good because
1/n! gets very small
very quickly. So let's just put down all
the numbers in sight here. If we focus on
the zeros in the estimate for the error
it seems clear that our approximation
will be correct in the first
four digits, right, and it is. So this
means that if we wanted to have some fun
calculating the first 1 million digits
of e from scratch, to pinpoint how many
terms of the infinite sum we'd have to
add we simply have to figure out which
number we have to substitute 7 by to get
a million zeros at the beginning of the
estimate at the bottom. Can someone
discuss in the comments why, just going
with what I've shown you so far, one
might want to aim for a million and one
zeros instead of just a million.
Anyway, in this way you can figure out
that you have to add a little more than
the first 205,000 terms of the infinite sum
to be able to guarantee a million
digits of e, very neat, right? And maybe
surprisingly the sort of thinking that
went into all this is also very
applicable. In fact, you use infinite sums
and estimations like this all the time
to come up with approximations of
complicated numbers that are accurate
enough for practical purposes.
It also turns out, and this really is
very surprising I think, that this
estimate for the error also gives a
straightforward way to prove that e is an
irrational number, that no fraction is
equal to e. Are you ready for some real
magic? Okay, so let's summarize what we've
done so far like this. On the left side
we have the difference between the true
value and the approximation, that's the
error, right? And we've seen that this
error is less than 1/7!
Now let's warm up by using this
inequality to show that one particular
fraction, 19/7 is not equal to e. Why 19/7 ?
Well, it does not really matter what
fraction we start with. The only reason
for us using 19/7 is that it has a 7
in the denominator which will mesh in
nicely with the other 7s that are
already floating around here. Can e be
equal to 19/7 ? Well, let's assume it is.
Then we've got this inequality up there.
19/7 minus the junk in the brackets is
less than 1/7!
Okay, now all the denominators on the
left divide 7! , right? Just
think about it for a moment. Yes they
divide 7! which means that we can
combine the left side into a fraction
with denominator 7! where
the ? stands for 1 or 2 or 3 or some
other positive integer. So IF 19/7
was really equal to e, THEN we just
showed this fraction, the error would
be 1/7! or larger. But, and
this is really the punchline, we already
know that the error is definitely
smaller than 1/7! . So our
assumption that 19/7 is equal to e
implies a statement that is obviously false.
So this means that our assumption, that
19/7 is equal to e must have been
false to start with. Tada! Okay you
probably didn't see that coming, right? To
show that e is not equal to any fraction
a/b we simply have to adjust our
argument like this: first replace 19/7
by a/b. Then, instead of summing up
to 1/7! we sum up to
1/b! . The estimate then also
changes to 1/b! and this
statement down here is still impossible
which implies that no fraction can be
equal to e or, in other words, that e is
irrational. Now you may have to watch
this part of the video again to really
get what is going on here. What makes
this proof work is the fact that the
close approximation to here on the left
is super close in the sense that it can
be written as a fraction that differs
from e in less than 1 over its
denominator. Similar super close
approximations to pi and other
irrational numbers also play a crucial
role in proving the irrationality and
transcendence of these numbers. Actually
a video on transcendental numbers is
next on my to-do list, so stay tuned.
The Simpsons singing nonsensical stuff...
(announcer) Tonight's Simpsons episode was
brought to you by the symbol Umlaut
and the number e, not the letter e but
the number whose exponential function is
the derivative of itself. (Mathologer) Hmm, the
exponential function is the derivative
of itself. Before I deal with this
congratulation to Homer and you for
making it this far. For this last part of
the video I'll assume that you do know a
little bit of calculus. In particular
I'll assume that you know what the
derivative of a function is. If you need
an introduction or a refresher check out
this video up there and then return here
or just sit back and admire the
mathematical magic doing its thing. Okay
we want to convince ourselves that the
exponential function is the derivative
of itself. Because of this identity the
derivative of the exponential function
is just the derivative of 1 plus the
derivative of this term plus the
derivative of that term, and so on so.
What's the derivative of x cubed divided
by 3! for example? Let's see: 3!
is 1 times 2 that's 2!
times 3. The derivative of x
cubed is 3 x squared. The 3s cancel
and of course what remains is equal to
this term here. So the derivative of x
cubed divided by 3! is simply
the previous term and you can check that
the derivative of that previous term is
the term before that. And the derivative
of that term is 1 and the derivative of
1 is 0, and so on. And so you can see that
the derivative of all the junk on the
right side is again the right side which
means the exponential function is its
own derivative. Fantastic, right? So, if you
made it up to here there is no reason to
stop. Let's use this insight for something
fun. The natural logarithm
log X is the inverse of the exponential
function. This means that e to the log X
is equal to X. Let's find the derivative
on both sides. The derivative of X is 1
and the derivative on the other side,
well we need that exponential function
its own derivative and the chain rule
for that but then we get this.
Now we have a close look and you see two
bits that are the same which means we
can also write X down here. Now divide
and we've got one of those super famous
facts from calculus, that the derivative of
log X is 1/X. Wonderful! And now I'm
just going to go for it. So integrate and
we get this guy here. We substitute e for
X and that gives this guy here. Now on
the right side we've got log e and
obviously that's equal to 1 since our
logarithm is base e. Almost there !
The standard geometric interpretation of
this definite integral here is that the
area under the graph of 1/X between
1 and e is exactly equal to 1. Now many
people are under the impression that, unlike
pi the number e does not have a nice geometric
interpretation. Well here we've got one,
right, in terms of the hyperbola which is
both the graph of 1/X and a basic
geometric shape closely related to pi's
circle. This is the way to remember it:
open up this yellow curtain here under
the hyperbola until it's area is exactly
one and you've found e. All right, now to
wrap things up I'll quickly sketch how
you can also use our infinite sum
identity to derive e to the i pi is
equal -1 and that's the
standard way this is done in calculus. There are also
ways to write the sine and cosine
functions as infinite sums like this.
After substituting i X for X in the top
identity and multiplying the sine
identity in the middle by i we've got
exactly the same stuff in the purple
and the blue boxes. Now since we're
dealing with identities, the same has to
be true on the left. So the contents of
the purple box is equal to the sum of
what's in the blue box, and this is
Euler's formula, super famous, right? Now
I go over all this slowly in this other
Simpson based video up there. So if you,
you know, want it a bit slower, check it
out. After plugging in pi for X the
right side becomes -1 which then
brings us full circle back to Euler's
identity. If you've made it this far
you've really earned yourself the
Mathologer's extra huge seal of approval.
So, as usual, I'm very interested in
finding out how well all these
explanations work for you. So please let
me know in the comments. And that's all
for today.
-------------------------------------------
Unpacked: Investing in Infrastructure - Duration: 4:03.
Hi my name is Adie Tomer
I direct the infrastructure portfolio at the
Brookings Institution's Metropolitan Policy Program
and I love researching infrastructure policy
because it's a sector that everyone uses every day.
Throughout the presidential campaign this past year
between candidates Trump and even candidate Clinton
we heard so much about infrastructure policy.
In fact infrastructure was more of a topic than
it's been in any presidential campaign
in recent history,
and with good reason.
We see infrastructure every day across our built environment
struggling in certain ways.
More and more Americans are
driving than ever before.
After a dip during the great recession we've set
more than three trillion miles of total driving
on our roads.
At the same time we're
seeing public transportation agencies
looking for more buses and more trains
and more investment needs.
So there's just more and more demand
on our roads.
Our freight networks are more important than ever.
We move more than 20 trillion dollars worth of goods,
and that's not just the computers
and other equipment you see in your offices
and of course the coal that we mine
to the agriculture that we harvest,
it's frankly all the consumer goods
that many of these days
get delivered directly to your house.
It's the groceries that you
shop to put in your refrigerator
and they're really expensive
and unfortunately about eighty percent
of those goods move along just ten percent
of trade corridors.
So next time you're driving through New York or Houston
or Dallas or San Francisco,
and you're wondering what all
that traffic is due to
part of it is all the goods that you're
demanding at home.
At the same time we're
seeing a significant amount of
investment needs in our water infrastructure.
Even though water is still flowing extremely well
into our homes and into our businesses,
we're talking about over 600 billion dollars
in investment needs.
But here's the real kicker,
only seventeen percent
of municipal water agencies even think they
have the capacity to make these investments.
So what we're confronted with
is that soon the tap inside your house
may not come out with the water that you need.
So the question is,
if infrastructures matter so much
how are we going to make sure
that we can find the investment capacity to rebuild America
for the next century of economic prosperity?
One of the biggest misnomers going on
not only in Washington D.C. circles today,
but frankly in the national media
is this concept of an infrastructure bill.
and in many ways it makes a lot of sense.
In particular we
heard Canada and now President Trump
talk about an infrastructure bill
ad nauseum, frankly.
It was one of the biggest ideas
even into his inaugural speech.
We've heard Speaker Ryan and
Majority Leader McConnell talk about
infrastructure potentially being on the docket
and continue to talk about it
as some kind of singular thing that
we're going to execute.
But here's the dirty little secret,
there is no such thing as an infrastructure bill.
In fact, throughout our entire federal government
apparatus, we're actually set up to
really do infrastructure in different sectors.
So think about it like this:
Congress has multiple committees in each
of the chambers that each deal with
issues ranging from transportation
to energy, to water, to telecommunications
it's almost exhausting even saying them all.
Now the problem is
how can you get these groups to talk together?
You're effectively asking for congressional
Tower of Babel if you expect that an
infrastructure bill is going to get passed.
But here it actually gets worse.
The executive agencies are also built around
these same silo groups.
So how are you going to get folks
from different committees in Congress,
different executive agencies
all to come together
to even agree on what an infrastructure project is?
But let's say we find the money somehow,
well that's the issue,
there's no money around.
Are we going to take more money from repatriation?
Well, Paul Ryan's already effectively pegged that
to pay down for a decrease in corporate taxes.
We could go the route of
just having the infrastructure tax credit
but we've already seen rural
senators say that's not going to work
for their state because they're probably
not going to get projects from the
private capital markets.
What we're really left with
is a system where folks are
asking for an infrastructure bill,
but they don't yet realize that it's not coming.
-------------------------------------------
U.S. Army Studies 'Third Arm' Device for Soldiers - Duration: 0:57.
For more infomation >> U.S. Army Studies 'Third Arm' Device for Soldiers - Duration: 0:57. -------------------------------------------
Investing for Passive Income with Brendan Kelly - Duration: 17:55.
The conversation today is all about life and money it's all about how much do you need
to retire comfortably or retired early
I guess the best way to start this conversation is if we go back in time and we look at our
lives from the beginning of when we start to earn money to when we can finally declare
to ourselves we have enough.
If I reflect on my life for a moment my early money making day started out as an employee
I worked casually on Elwood beach in Victoria selling soft drinks needless to say at the
age of 15 I wasn't particularly school so my rate of exchange of time for money was
really quiet poor.
But it did introduce me to the idea of what employment was an employment is just that
it's an exchange of time for money and over a period of years I learnt that if I skilled
up if I specialised I was able to create a better exchange rate as I worked through school
and then through uni I finally got a degree as a teacher of math science computer science
having that skill allowed me to improve my rate of exchange better than that of selling
soft drink cans at a beach.
Well at the age of 22 that offered me a new found freedom I was pretty excited I was out
of home I was into my own car and happen to be a 1972 white Toyota Corolla Coupe admittedly
it was held together by wire and rope but it was still a car it was mine and I had my
freedom was pretty excited I was out of home life was wonderful but over a period of years
I recognise that there's a vulnerability to employment given that I am exchanging my time
and skill for money it doesn't matter how skilled I become if I can't put my time and
I'm not going to earn any money let me ask a question if you were no longer able to spend
time in your job what would happen to your income if you were no longer able to commit
time as a self employed person what would happen to your revenue or if you're running
a business that still heavily dependent upon you and you were not able to commit the time
what would happen to the business and in that we are living with a vulnerability so if we
look at this differently and ask a different question we might then get to see the significance
of the vulnerability that we facing as an employee has a self employed person or as
a business owner where the business is still heavily dependent upon us being there
what is retirement?
well retirement is your ability to earn an income without putting the time in so the
answer to having a better life the answer to Early Retirement or retire and comfortably
comes in our ability to create a system whereby we are no longer needing to exchange it time
for money so how do we do that what's the solution
the solution is simply to build an asset base but is there a right and wrong asset base
to be building.
If I had a 5 million dollar home and no income is this the sort of asset base that I'd want.
And the answer is no I might be living in the Taj Mahal but I'll be living on baked
beans and that's not the life I want to live.
What I'm after is an asset base that somebody else wants to use because if somebody else
wants to use it then they will pay me to do so in that I am generating an income stream
now if my acid base is big enough and people are willing to pay me enough then there will
come a point where I will no longer need to exchange my time for money in order to live
the life I want before the power of this really hit home for me I thought that my time with
better spent being a better employee so I spent my time skilling up I spent my time
learning about what it was to be a great employee how I can be indispensable to the company
or how I can be eminently re employable if it was it something occurred and I was no
longer able to be employed in the company that I was working for at the time.
And by doing that I thought I'd mitigated the risk of exchanging my time for money when
in fact what I've done was Focus my energy on entirely the wrong thing you see what you
think it determines the outcome of your life and let me see if I can explain it a bit.
when I was an employee looking to be a better employee I thought about being a better employee
as a consequence I make decisions about being a better employee as a consequence of those
decisions I took action to being a better employee Those actions that I've taken the
outcome was that I was a better employee goal accomplished except that's not the goal I
need to accomplish if I want to retire early or retire comfortably
The goal but I need to accomplish is to be better at building my asset base and that's
an incredibly powerful shift in thinking if I begin to think And begin to think about
being better at building an asset base then I start to make decisions about being better
at building an asset base as a consequence of those decisions I begin to take action
to be better at building an asset base and as a consequence of that action I have achieved
an outcome I am better at building that asset base and as a consequence of being better
at building that asset base I've been able to quit the rat race now that was a really
powerful shift for me and that is the exact same shift that's available for you it starts
out very subtly but the impact in your life could be phenomenal if you shift your thinking
from being better at being employed being better at being self employed or being better
at being dependent in your business and work on think about create ideas around being better
at building an asset base.
And if you continue to apply that focus, then you will continue to grow in your wisdom and
your ability to build a phenomenal asset base.
An acid base that will allow you to retire decades early or retire extremely comfortably
let's start to make that real and it leads into today's topic how much is enough
so we now need to figure out how big this asset base needs to be in order to allow us
to retire early or comfortably and as with most goal achievement it begins with the end
in mind the end here in this instance is how much income would you be happy to live off
how much income is enough for you to retire early now there are a couple of ways we can
calculate this one is to think about everything you want in your life and the lifestyle you
want to live it up all of the costs associated in a 12 month time frame to achieve that and
that would represent what you would need to earn in a year another alternative might be
just to pick a flat figure like for example a hundred thousand dollars a year if I had
$100,000 a year and no debt that would be a fairly comfortable way to go for some people
over $100,000 is either too much and unrealistic or not enough and and that expect more so
another way that you might like to figure out how much is enough for you would be to
think about what you're currently earning in a year and add a bit
so if your on $50,000 a year you might wanna make that 55 or $60,000 a year and use that
as your line in the sand for how much you'd like to accomplish as a passive income or
an income that your earning from your asset base for the sake of simplicity though I'm
going to choose $100,000 a year as an example to help do the mathematics so that you can
apply the same approach to the income that you're interested in earning
Now if we've got an asset base and someone is willing to pay us $100,000 a year that's
going to represent a certain return on investment or rate of interest now depending upon your
level of sophistication and skill that rate of interest becomes quite variable for some
it will be 2% someone to be 4% for some it'll be 5 for some it'll be 8 for someone to be
10 for someone will be 20.
So I'd like you to think about what you think would be a fair and reasonable return on investment
that you think you might be able to get.
For me I'm going to pick 8% so if I'm going to earn $100,000 from an 8% return on investment
what is the size asset base that I'm after well simple mathematics suggest that all we
need to do was divide $100,000 per annum by 8% and in doing so we achieve an asset base
requirement of 1.25 million dollars.
now as a property coach and mentor when I said this I deal with people the reaction
has been quite different for some the reaction is just 1.25 wow that's easy I could do that
really quickly for others it's 1.25 that's impossible how can anybody achieve that.
it doesn't matter what your feeling right now around your ability to achieve that what
matters is the numbers what matters is the goal that we looking to achieve so if I had
1.25 million dollars of income producing assets with a return on investment for about 8% then
I would be earning $100,000 a year so if we now take your example think about the income
that you want to earn as a passive income think about the rate of return that you think
you can get divide your income by the rate of return and this will give you an idea of
the asset base do you need in order to achieve their now if you think that I said base is
too big then we might need to make some adjustments and you can do so by increasing the rate of
return and learning how or reducing the amount of money you want to earn in any one year
and still be comfortable but I'd like to suggest that there is no need to be fearful about
the size of the acid base that you're looking to achieve because as property investors we
are problem solvers and by declaring the size of the asset base that we are after with just
simply seeing a problem A job now is to solve it
Well I guess the next question then becomes how do we achieve that it's great to know
that amount but how do we achieve it how do we get that much money in our bank account
if we are able to siphon off some of that time and some of our money so that we can
spend our energy on building out wisdom building our knowledge being able to buy the right
property being up to follow through on our projects and our purchases and being able
to deliver a profit and an income then we will create an asset base the size that we
need
let me ask a different question now where do you think your biggest risk in achieving
this asset base is well the idea of creating an asset base is a great idea it is just an
idea until it is a reality and the human mind is very very good at rationalisation so while
you may be engaged in the idea of building an asset base now it's very easy for life
to push back and get in the way in our conversation so far we've done some math and talked some
numbers and I encourage you now to think about your reaction during those conversations because
again when I speak to people on this there are some common reasons justifications excuses
for why they may not be able to achieve that the first is the lack of I don't know enough
I don't have enough money to get started I don't have enough time my life is full of
those things problems well yes they are if you don't believe you know enough then guess
what you don't know enough if you don't believe you have enough money well guess what you
don't have enough money if you don't believe you have enough time well again guess what
you don't have enough time and therefore for you these things are very very real I appreciate
that but has property investors we are problem solvers so my question back to the people
who raise these concerns is is I don't know enough a problem with a solution and invariably
the answer is yes there is a solution to not knowing enough is there a solution to the
problem of not having enough money again yes there is is there a solution to the problem
of not having enough time again yes there is so each of these common problems do have
solutions and it taps into why your investing if you have a strong why then you'll be interested
in finding the solution and you'll be keen to know what that is if you've not tapped
into why your investing then you might find at the size of a problem you think you're
facing feels overwhelming and therefore you stop dead.
My encouragement to you is to try a process of thinking where there is no problem that
doesn't have a solution and rather than focus on the problem focus on the creation of a
solution and in that you get to keep going in that you get to continue to create and
in that you will achieve the asset base that you after to retire early and retire comfortably.
Now before we close off today's conversation, I'd like to raise one more alarm bell for
what might get in the way for you, and that might be procrastination.
procrastination comes in many different forms it comes in the form of distraction or putting
things on hold or thinking about it tomorrow or just putting it down and not persisting
procrastination takes many many different forms and as an idea I would encourage you
to be vigilant to observe yourself watch yourself as you progress on this journey to achieving
great wealth that you are not waylaid by procrastination watch yourself as you get distracted watch
yourself as things get in the way and you engage inside line issues because anything
that can take you away from your time to creating an asset base adds time to the creation of
that asset base so retiring early becomes less early retire and comfortable it becomes
less comfortable to achieve what you want to achieve requires a certain vigilance a
certain persistence and I would encourage you to take on the idea of you can have anything
you want but be persistent with it you can have the asset base that you're after but
be persistent with it you can have the passive income you want but be persistent with requiring
be persistent with building it be persistent with learning how to create that and if you
do then you have a life far better than you think you can have right now.
Until we meet again invest wisely.
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