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>> No.7996069 [View]
File: 142 KB, 907x960, triple fields are the new triple integrals.jpg [View same] [iqdb] [saucenao] [google] [report]
7996069

well i'm off to bed, but i'll just go ahead and say
if you've defined the numbers like i did here >>7995958
and assigned the symbol "1" to the element [math] \{ \emptyset \} [/math]
then 1 = 1 follows directly from the axiom of extensionality

[math] \forall{A}. \forall{B}. (\forall{C}.(C \in A \iff C \in B) \implies A=B) [/math]

which says "if you take any sets A and B, and if for every set C, C is in A only if C is in B, then A is equal to B"
which, put less autistically, says "if A and B have the same elements, then they are equal"

so there's my first proof that 1 = 1

i get bored in class and do a lot of messing around with foundations and low-level stuff so i've got a lot more of this if anybody's interested

i kinda want to post it all TЬH but i'd rather post it in a thread where there's interest
i have category theoretic and type theoretic proofs that 1=1 as well, but they're pretty much the same as that proof up there^

also can somebody tell me where pic related is from?
i've image searched it and stuff but i can't find anything
i just want to know why the dodecahedron group is off by itself as if it's as important or even as interesting as

>> No.7947480 [View]
File: 142 KB, 907x960, Holy Shit.jpg [View same] [iqdb] [saucenao] [google] [report]
7947480

Do you guys have cool diagrams that sum up different areas of maths into one neat space ?

pic related : example

>> No.7046784 [View]
File: 142 KB, 907x960, Holy Shit.jpg [View same] [iqdb] [saucenao] [google] [report]
7046784

So I saw this (attached picture) relationship on another thread .

Does anyone else have a similar illustration, which shows the relationship between different branches of maths ?

>Mathematics

>> No.7046004 [View]
File: 130 KB, 907x960, math.jpg [View same] [iqdb] [saucenao] [google] [report]
7046004

In the meantime, I will self-bump with good visuals and links that have helped me, for any /sci/ browsers out there that teach themselves things.

>Analysis
https://59clc.files.wordpress.com/2012/08/real-and-functional-analysis-lang.pdf

http://classicalrealanalysis.info/com/documents/TBB-AllChapters-Landscape.pdf

>Engineering Textbooks
http://kisi.deu.edu.tr//ali.sevimlican/Peter_V__O%27Neil-Advanced_Engineering_Mathematics,_7th_Edition__-Cengage%282011%29.pdf



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