![toruses[1].jpg](https://i.imgur.com/aEjXeJ3.jpg "toruses[1].jpg")
is topology a meme ?
>>7955945
Asking "is X a meme" is a meme.
>>7955949
stating "[asking] 'is X a meme' is a meme", is a meme
>>7955945
It's homotopy equivalent to a meme.
>>7955966
stating "stating "[asking] 'is X a meme' is a meme", is a meme", is a meme.
>>7955970
/thread
Let m(x, n) be a function defined as follows:
n is a non-negative integer
x is some sequence of characters
m(x, 0) = "x is a meme"
m(x, n) = "m(x, n-1) is a meme" (for n != 0)
m(x, n) is a meme for all x and all n.
>>7955980
n! =/= 0 for all non negative integers though
>>7955980
Stating:
"Let m(x, n) be a function defined as follows:
n is a non-negative integer
x is some sequence of characters
m(x, 0) = "x is a meme"
m(x, n) = "m(x, n-1) is a meme" (for n != 0)
m(x, n) is a meme for all x and all n."
is a meme.
>>7955980
>mixing operations and predicates like that
How come my computer doesn't show (math) and (/math) text? If you replace the brackets by [ and ], I just see the text. How do I make them show?
>>7955983
:^)
>>7955988
HE DID IT THE ABSOLUTE MADMAN
>>7955988
"Let m(x, n) be a function defined as follows:
n is a non-negative integer
x is some sequence of characters
m(x, 0) = "Let m(i, j) be a function defined as follows:
j is a non-negative integer
i is some sequence of characters
m(i, 0) = "i is a meme"
m(i, j) = "m(i, j-1) is a meme" (for j != 0)
m(i, j) is a meme for all i and all j."
m(x, n) = "m(x, n-1) is a meme" (for n != 0)
m(x, n) is a meme for all x and all n."
>>7956076
You spent like 1 hr on that amiritw
>>7956084
n-no
I'm taking an introductory course on topology next semester, and after reading some stuff about it online I'm still not 100% sure what topology is the study of
>>7956431
There are a few ways to look at it. It gives a way to talk about points being "close together" even when it's impossible to give a quantitative distance between them. As a result, topology is pretty ubiquitous any time you want to talk about geometric spaces in math.
This also allows you to define continuous functions as broadly as possible, which in some sense makes topology the study of deforming objects nicely -- stretching out objects as if they were made of putty is a continuous map so long as you aren't ripping/tearing/whatever.
![link[1].jpg](https://i.imgur.com/y6SlGcE.jpg "link[1].jpg")
>>7956431
>>7956431
study of neat pictures yo
>>7956431
I'm taking one right now. It's like my Real Analysis course but being even more rigorous with definitions.
So far we learned what it truly means for a set to be open or closed. Took a lot of time to get to this point because we spent most of the course on redefining continuity and limits to a more general argument that can be applied to any case. We also learned what it means to say something is arbitrarily close (i.e. adherent), and sequential compactness.
Some really tricky proofs, intuition fails you at times and it's all about forcing you to follow definitions closely.
>>7957137
>being even more rigorous with definitions.
I think you don't know what the word rigorous means.
>>7956431
Topology is the study of topological spaces.
>>7955945
[math]\operatorname{index}\gamma^{\mu} D_{\mu}= -\frac{1}{8\pi^2}\int_{M}\operatorname{Tr}\mathcal{F}^2[/math] is the biggest meme of all time
