/sci/ - Science & Math

>>12367198
>Finite set edition
Assume the Axiom of Pairing, Infinity and Separation and the Law of Excluded Middle.
Denote by [math]{\mathbb N}[/math] our model of the naturals and denote the Continuum Hypothesis by [math]{\mathsf{CH}}[/math].

Consider
[math]S_{\mathsf{CH}}:=\big\{n\in{\mathbb N}\mid (n<5) \lor {\mathsf{CH}}\big\}[/math],
a subset of [math]{\mathbb N}[/math].
Either [math]{\mathsf{CH}}[/math] or [math]\neg{\mathsf{CH}}[/math]. In the first case, [math]S=\{0,1,2,3,4\}[/math] and in the second, [math]S_{\mathsf{CH}}={\mathbb N}[/math]. The identity in either case is a bijection to a finite resp. countably infinite set.

We conclude that [math]S_{\mathsf{CH}}[/math] is either a finite or an infinite set.

Do you agree with this fine piece of math?

https://terrytao.wordpress.com/2020/10/04/foundational-aspects-of-uncountable-measure-theory-gelfand-duality-riesz-representation-canonical-models-and-canonical-disintegration/

Is there a nice closed formula for

[math] \sum_{k=0}^{m-1} \dfrac{n!}{(n-k)!} [/math]

?

Mathematica sadly assumes non-natural values and returns something something EiIntegral (even if I simpify assunming m and n are ints), but there might be a nice number assuming they are ints.

https://www.nytimes.com/2020/06/05/opinion/sunday/free-college-tuition-coronavirus.html

Given me a simple to understand problem (the statement of it being understandable), which can only be well solved with algebraic geometry methods post 1950.

Let me phrase it different: Give me a problem that Poincare and Hilbert would have stated, but where they would be interested and surprised about the method of solution.

Why is Bobby such an asshole?
And why is Magnus so unsympathetic as well?
And what do I have to do to bone Botez?

https://youtu.be/WPzrLWNbuzo

>>11797246
>Girls like creative types far more.
Everybody likes creative types far more.

"IQ" in the sense some diligent sperg who does logic all day because he has no friends is not very tied to a happy life.
That said, a lot of people are in math and do creative work there.
Sad truth is just from knowing a lot of math, doesn't mean you're "good" at it. Knowing a lot of math doesn't help and is especially pathetic if you're asocial at the same time. They can go together.

>>11797283
Thoughts:
One solution is y(x):=x, so the intersection must be at (X,X) for some X.
The definition is symmetric in x and y, so I suppose we must have y'(X)=-1.
Maybe that and taking the derivative of [math] x^{y(x)}\cdot y(x)^{-x} [/math] helps in finding X. Maybe an exponential ansatz assuming information from the solution.

>>11692322
>>11692323
I was never a fan of this witticism, given [math]=4[/math] subsumes the other two.

https://vixra.org/pdf/2004.0065v1.pdf
https://vixra.org/pdf/1502.0038v1.pdf