Transcendental Numbers (extra footage) - Numberphile

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Информация о Transcendental Numbers (extra footage) - Numberphile

Название	:	Transcendental Numbers (extra footage) - Numberphile
Продолжительность	:	3.09
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Просмотров	:	287 rb

If it's possible I think I might have broken the seal from watching this short video I'm not concerned with approximations, I want to know what is
Comment from : @robertstevensii4018

Simon is a legend
Comment from : @lukeszklarz9674

Doesn’t this just go to show that, despite all of its power, algebra is simply not a sufficient tool to describe all of reality? Not even most of reality, apparently, if most numbers are transcendental Algebraic math just becomes a window that you can peer through
Comment from : @DannyWrigley

Thanks!
Comment from : @dushyanthabandarapalipana5492

As soon as Cantor showed there was a bigger infinity of real numbers, Ie that there are uncountably many, the countable infinity of algebraic numbers gets swallowed up This makes the uncountable infinity of transcendental numbers a certainty, even if you can't yet actually prove a particular number such as e or pi to have that property We can be surrounded by a large majority of numbers without being able to identify one Mind blowing!
Comment from : @peterhawes9680

Interesting: there are uncountably infinitely many irrational numbers There are countably infinitely many algebraic numbers Yet the algebraic numbers include some irrationals (if n is an integer, the nth root of any positive integer, if not itself an integer, is irrational The proof goes just like the proof for the square root of two) Which means that most irrational numbers (in fact, uncountably infinitely many of them) are transcendental And clearly every transcendental number is irrational
Comment from : @chrisburges4160

This guy looks exactly like what I imagine an ancient Roman would have looked like
Comment from : @kengonagaoka1968

I thought the video continue much longer :-) Nevertheless love this guy and his saying " I am not interested in approximations ", as many comments pointed it out :-)
Comment from : @Prasen1729

Mathematician: pi is 31415brEngineer: pi is 3, sometimes 4 if I feel special that day
Comment from : @adriangiurca4901

Is planck's constant transcendental? Or some other known physics constant?
Comment from : @_kantor_

Does anyone know if Fibonacci (the man, as in Leonardo Pisano) was interested in or wrote about squaring the circle? I'd really like to know x
Comment from : @c4cathyd

Physicians are gonna hate for that last sentence xD
Comment from : @armycin

ppl often overrate maths, it's just a study of a tool On the other hand, physics is a study of an atom to the universe using the tool Maths I think physics is more exciting even if we have to approximate some values to understand things :)
Comment from : @sky-xk5be

this is awesome!
Comment from : @lua3

The algebraic numbers form a set of measure 0 on the real number line A way to think of it is if you had a dart with a point so fine it could hit a single number and you threw it at the real number line, your chance of hitting an algebraic number would be 0
Comment from : @TIO540S1

pi^0 - 1?
Comment from : @JackFlead

stop blowing my mind! :D
Comment from : @Ashm00r

Pi is 22/7
Comment from : @GeodesicBruh

More than 2000 years
Comment from : @marklapolla2638

"I'm not interested in approximations"brbrObviously you're not a golfer
Comment from : @uraldamasis6887

there is one perfect circle Maynard is the singer XD
Comment from : @pupperemeritus9189

are transcendental numbers still transcendent even in transcendent base ?
Comment from : @williamgingras304

I was hoping this would just be a loop of him saying that pi is 22/7
Comment from : @Cernoise

Given that e and pi are both transcendental, and they are both non repeating (in the mathy sense of the word) non terminating decimals, could we say that any given non repeating non terminating decimal is transcendental?
Comment from : @cubethesquid3919

noice
Comment from : @steffen5121

I love hearing "I'm not interested in approximations" and the admiration of "sharp" equations just after hearing Matt wax sentimental on the rounding of powers of ϕ
Comment from : @mrnicomedes

transcendentals are just glitches in the program "Universe" :P
Comment from : @scubahick

PLEASE DO AN EXPLANATION OF EULER'S IDENTITY NOT USING THE MACLAURIN EXPANSION OR OTHER TRICKS WHICH DON'T EXPLAIN ITS TRUE NATURE
Comment from : @councilhousecaviar

I love watching these guys get so excited by maths
Comment from : @finalcountdown3210

Trandenscental
Comment from : @TimmehTRP

Dear christ, MATHEMATICS ISN'T a plural word It's a singular concept So saying "Maths" isn't correct There aren't multiple "maths" that you're studying You're studying "Mathematics" which is a singular term to describe the multiple disciplines under an umbrella It'd be like suggesting that someone doing Anthropology was getting his "Sciences" degree As though the various sciences weren't under one BIG UMBRELLA term to distinguish them This is not written by an English snob It's written by someone who understands roots and suffixes Get a grip
Comment from : @rayh966

I'd like to like this video again But Youtube don't allow it
Comment from : @ShapeDoppelganger

so the universe must be related to absolute constants by number qualities, but always flows continously, ie, has inherent uncertainty that trancends solid states? Seems like an eternal now, functionally
Comment from : @davidwilkie9551

im the (numberphile)phile
Comment from : @GrantJolanta

What was that fuss about the "29 decimals"?
Comment from : @Kriegerdammerung

Nice
Comment from : @konnichiwa7925

Pierfection
Comment from : @MrEolicus

Are algebraic numbers countably infinite? I thought they weren't cause there are an infinite amount of rational numbers between 0 and 1, or between literally any two pairs of rational numbers, thats without bringing irrational roots and complex numbers into the mix with the rest of the algebraic numbers How are they countably infinite? (I reckon this was just a mistake, right?)
Comment from : @triplebog

More on Euler, plz
Comment from : @samwise2588

is there an algebraic equation of more than one transcendental number yielding an integer ? (except of course the product with itself)
Comment from : @TheGamblermusic

I wonder if someone could work out what proportion of ℝ is transcendental
Comment from : @ar_xiv

MORE SIMON!!!!!
Comment from : @eboodnero

amazing!
Comment from : @tassietraveller2239

TheGeneralWolf a real number is simply a number that has no imaginary part that is, it is either rational, or irrational, with no imaginary part So Pi is still a real number It just can't be solved algebraically
Comment from : @Elitekross

TheGeneralWolf Pi is still a real number Transcendental numbers can still be real numbers because they have a 'place' on the real line in basically the same way that the integers have a 'place' Numbers are not real if they cannot be represented on the real line, such as sqrt(-1) and infinity
Comment from : @henrymaguire43

loved it when you said "i'm not interested in approximations" , i agree calculus is not real maths :)
Comment from : @kirofars

"I'm not interested in approximations" spoken like a true mathematician, I love this guy
Comment from : @Quantiad

The General Wolf, pi is real and transcendental Also, exactly 2 plus exactly 2 does equal exactly 4
Comment from : @andrewwesleyhudson5983

Pi is real, it's just not algebraic
Comment from : @exoticuhh

"I m not interested in approximation" Wow Very interesting way to see things!
Comment from : @andrasescninelovidiu9294

When the Lord was handing out brains the mathematician thought he said trains and so he took his out and played with it
Comment from : @taxigringo

i(pi)^(1/2)
Comment from : @t3hgir

I'm giving up arguing with you as neither of us will change our reasoning All of the discussion aside, have a good day, it was nice to have an intelligible discussion
Comment from : @georgepenwarden5650

Well, you would end up with an imaginary root vegetable based pie, like a potato pie However, defining a pie by the vegetable used is not very helpful, as it suggests that the main ingredient is that vegetable, when there could also be onion or some sort of meat like lamb mince In that case it would be best to call it a lamb mince pie, but since we are dealing with a root vegetable based pie, I think it would be quite bland While I wouldn't eat it, since it is imaginary, it doesn't matter
Comment from : @georgepenwarden5650

There is a degree symbol ° for a reason as far as I am concerned Really the ≡ symbol is known to me as congruence and sometimes as a definition, so I am not sure what you are refering to Really of course the parts of an equation need to be well defined But often the same equation can be derived in multiple ways And as long as the way is valid and logically consistent, it doesn't matter which way was taken
Comment from : @nezrif27

i√π
Comment from : @Corpulous

So pi itself, the number with no units, is not transcendental, but pi radians is? Would that make 180 degrees transcendental? If it does, I now understand Thank you for understanding my point
Comment from : @georgepenwarden5650

Pi is the circumference of a circle divided by the diameter of that circle Pi may play an integral part in measuring angles in radians, but it is still a number
Comment from : @mid_packs

That's kind of the definition
Comment from : @georgepenwarden5650

I'd give you an additional thumb up, but right now the total ammount is a perfect power of 2
Comment from : @TechMetalPenguin

It just turns out that not only exp(i * Pi) equals -1, it also does happen that in polar coordinates, the angle of that complex number is Pi It's kinda shocking because it all fits but math sometimes does this to us, it's like christmas
Comment from : @Hyo9000

truncation always works, makes rational
Comment from : @arado240dd

In radians, pi is a ratio, not an angle
Comment from : @larrysbeerbarn

If you want, I could message you a proof In order to do it justice, I will need more than 500 characters
Comment from : @MuffinsAPlenty

WHY are most real numbers trancendental??? WE WANT PROOOOOF!!!
Comment from : @ShadowDatsas

pi - pi doesn't follow the rules of the game (can only use whole numbers) Any number to the 0th power is kinda like multiplying anything by 0, as mentioned in the previous video It gives a blanket answer to all cases and "isn't very interesting"
Comment from : @yoshiyukiblade

No, you can't do that with e or pi, because the rule is that you can only do operations with whole numbers to reduce them to zero the proof shows that you can't do that with them
Comment from : @RPBiohazard

what does measuring have to do with that? good lord
Comment from : @JohannaMueller57

True, true
Comment from : @delilahwood3708

Not sure about this, but I think it's because Euler's Formula only works when cos x and sin x are defined in radians Didn't really understand this though
Comment from : @MozartJunior22

The way you are thinking it, pi is 314159 radians, which is a half turn when you muiltiply it by the radius of a circle However you are still using pi as the value that is 314159 that goes on forever!
Comment from : @jesuss9331

This dude is amazing
Comment from : @Whateverworksism

"I'm not interested in approximation" I love that guy because I feel the same way :)
Comment from : @xFabi99

Sine and Cosine Also, complex numbers in the exponential form are explaining the number by the modulus and argument, ie the length, and angle
Comment from : @georgepenwarden5650