/sci/ - Science & Math

So, if there is such a thing known as "pi", would you mind writing it down for me?

thanks in advance

If there is such a number as "Pi" as you claim, could you please write it down ?
Thank you.

> Rational parameterization of the circle
> Euclidean construction of multiplication of roots of unity
> The Stern-Brocot tree and algebraic numbers
> The fundamental DREAM of algebra
> Quadrance
> Calculates Bernoulli numbers by solving Pascal's triangle as a matrix
> The ILLUSION of infinite groups
> polynumbers/vexels/maxels

What is your favorite NJWildberger redpill

Will watching his videos on the foundations of mathematics fuck me over in the long run? I've watched a few now and so far he seems to make the distinction every time his theory goes against canonical maths.

>>9304535
>implying we didn't think you we're just baiting and being an attention whore the entire time

Best math channel

https://www.youtube.com/watch?v=dW8Cy6WrO94
I know a lot of people consider this guy a meme, or a god, depending on who you talk to, but I started checking out his videos and I really enjoy his lectures on the history of math. I like how instead of just explaining the concepts of certain civilizations he actually provides proofs and delves into the roots of the concepts. Anyone else watch this? What are your thoughts? I highly recommend checking this out, whether you like the man or not.

>>8977267
>degrees

The largest number which can be represented by no fewer than [math]10^{100}[/math] symbols.

What do I win?

>>8958792
>implying that pic related ain't the greatest

>hat says "split"
>doesn't believe in Dedekind cuts

Can somebody explain his problem to me?

Not including Wildberger would be a travesty.

What's the deal with Norman Wildberger ?
He just tells a bunch of pseudo-paradoxes in a series containing a fuckload of videos, is that enough for /sci/ to meme him out every instant ?

>>8641406
>>8641415
>>8641520
>>8641530
Not a number.

Real numbers

What's his fucking problem?

Prove convincingly to me that the real numbers exist.

Come on, /sci/, you should be able to do this.

What makes a number real?

If [math] \sum\limits_{n=1}^{|\mathbb{N}|} 2^{-n} = 1 [/math], then what does [math] \sum\limits_{n=1}^{|2^\mathbb{N}|} 2^{-n} [/math] equal?

Is he right, misguided, or a hack?

>>8133977
>I wonder who's behind this post

ITT we prove that the Kolakoski sequence has the same density of 1s and 2s.

It's defined as the unique sequence of only 1s and 2s starting with 12 such that the [math]n^{th}[/math] element defines the run length of the [math]n^{th}[/math] run of elements.

The sequence starts as follows: 12211212212211211221211. It's also not hard to calculate either once you're used to it, so don't get put off too fast.

Notice that when we group the runs of elements and create the sequence of their lengths, we recover the original sequence.

[1][22][11][2][1][22][1][22][11][2][11][22][1][2][11]

Taking the size of each bracketed group we get 122112122122112, which matches the original sequence.

Conversely, by grouping every pair of elements, and then expanding them with the following rules, we also recover the original sequence.

Here are the rules.

[math]11 \rightarrow 12[/math]
[math]12 \rightarrow 122[/math]
[math]21 \rightarrow 112[/math]
[math]22 \rightarrow 1122[/math]

Group every other pair of consecutive elements in the sequence, and then expand using the rules.

[12][21][12][12][21][22][11][21][12][21][21]
122112122122112112212112122112112

Again, we recover the original sequence.

Note that this last mentioned property can used to generate the sequence.

Also, better methods exist, with the best I've seen allowing you to calculate that [math]n^{th}[/math] element of this sequence using O(log(n)) memory rather than O(n) memory as the naive method hinted at above would use.

Let's do this shit senpaitachi.

https://en.wikipedia.org/wiki/Kolakoski_sequence
https://oeis.org/A000002

Prove the existence of the real numbers, /sci/

Protip: you can't