/sci/ - Science & Math

>>11265835
>Extensive knowledge of the Riemann Zeta Function
unneeded.

Jokes aside, the first 3 points are literally just the context in which the problem is already in, so there's no way around them.

I'd guess it's probably related to some ugly independence result.

If it has a modern proof at all, i.e. something along the lines of how all the other versions of the =1/2 statement for the other popular Zeta functions have been proven, i.e.
https://en.wikipedia.org/wiki/Weil_conjectures#Statement_of_the_Weil_conjectures

then yes, you need a category theory
(and a lot more specific things using that language)

It's the proposition you get from anti-social autists when the try to imagine a world where their status might be a little bit elevated, without knowledge of or through for human interaction otherwise.
It's cringe

>>7708352
If by "analysist" you mean a guy who's studying classical analysis, then the question has probably no answer.
Dropping non-constructive axioms of your theories becomes relevant, for example, whenever you got to implement stuff. As you can't even list the element of [math]\mathbb R[/math], theorems in classical analysis will be vacuous for such realization. The good news is that people have spun the spiderwebs of theories like analysis in a constructive fashion long ago, see for example all the constrictive theorems that aggregate around the unprovable intermediate value theorem

https://en.wikipedia.org/wiki/Constructive_analysis#Examples

Syntetic analysis as in the pic from the book by Kock is relevant because the requirements for the theory are such that certain topoi give you internal analysis as a gift. That is you consider some topos, check if it has this and that property and then it might be implied that that topos really is about calculus/contains a theory of calculus and you can import all the theorems you already know - I mean that's the nice feat of category theory in general.

The category of sets [math]A, B, C,...[/math] (=objects) and functions [math]f, g ,h,...[/math] (=arrows) is a topos and thus has cartesian product [math]A\times B[/math] (=the categorical product) and function spaces [math]B^A[/math] (=internal, setty realizations of the arrow class from [math]A[/math] to [math]B[/math], which may be written [math]A \to B[/math])
A theorem of sets is that the function space
[math] (A\times B) \to C [/math]
is isomorphic to
[math] (B\times A) \to C [/math]
as well as
[math] A \to C^B [/math]
and
[math] B \to C^A [/math]
E.g. for A=B=C the reals the first space contains
[math] \langle a,b \rangle \mapsto \sin(a)+3b [/math]
which you can systematically map to the function
[math] \langle b,a \rangle \mapsto \sin(a)+3b [/math]

I'm pretty sure JavaScript Front end developer, IT guys and server maintenance people are all counter to "Computing Jobs" there - it shouldn't be put against science there.
Besides, imho university shouldn't be seen only as job education. Surely, if you want to get something out of life it's fair if you're going to study Physics or Biology out of interest, while learning SQL isn't something you'd do as whole-heartedly.

>engineering degree
>maths

[math] \frac {1} {\sqrt x} - \frac {1} {\sqrt (x^2+x)} [/math]

[math] = \frac {1} {\sqrt x} \left( 1 - \frac {1} {\sqrt (1+x)} \right) [/math]

[math] = \frac {1} {\sqrt x} \left( 1 - \left( 1 - \frac{x}{2} + O(x^2) \right) \right) [/math]

[math] = \frac {\sqrt x} {2} + O(x^{3/2}) [/math]

[math] \frac {1} {\sqrt (x)} - \frac {1} {\sqrt (x^2+x)} [/math]

[math] = \frac {1} {\sqrt (x)} \left( 1 - \frac {1} {\sqrt (1+x)} \right) [/math]

[math] = \frac {1} {\sqrt (x)} \left( 1 - \left( 1 - \frac{x}{2} + O(x^2) \right) \right) [/math]

[math] = \frac {1} {\sqrt (x)} \left( \frac{x}{2} + O(x^2) \right) [/math]

[math] = \frac {\sqrt (x)} {2} + O(x^{3/2}) [/math]

[math] X_t = X_0 + \int_0^t \mu_s(X_s, s)\, ds + \int_0^t \sigma_s(X_s, s) \, dW_s [/math]