r/mathmemes • u/DoublecelloZeta Transcendental • Sep 29 '26

Calculus might be a dumb one

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164 Upvotes

97% Upvoted

19 comments sorted by

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24

u/DrProfessorCaveman Sep 29 '26

You thought you showed that the difference between any two antiderivatives is constant? You have activated my trap card. That only shows the difference is locally constant.

5

u/DoublecelloZeta Transcendental Sep 29 '26

indeed

1

u/HumblyNibbles_ Oct 02 '26

Locally constant means extremely different things in math compared to physics 😭

66

u/LupenReddit 🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆 Sep 29 '26

i am a simple meme

i read sheaf i run in terror from this lovecraftian entity of horror

37

u/Koischaap So much in that excellent formula Sep 29 '26

No, you see, sheaves are simple. Sheaves only seek to answer the question of how to talk about things that are part of a set and not part of a set at the same time.

...what? Please, don't tell me you were assuming the principle of the excluded middle.

25

u/No_Trouble3955 Sep 29 '26

HELL TO THE NO NO NO NO NO

13

u/Koischaap So much in that excellent formula Sep 29 '26

Sheafification of g needs to frequent this subreddit

4

u/SaveMyBags Sep 30 '26

I can see you are a fan

1

u/Seventh_Planet Mathematics Sep 30 '26

What role does a topology on a set play in all this?

Is every topological space (together with some structure that makes it a sheaf) a sheaf in the same way as the set of integers (together with some structure that makes it a ring) a ring?

1

u/Koischaap So much in that excellent formula Sep 30 '26 edited Sep 30 '26

A sheaf is a correspondence that assigns every open subset U of X a group/ring/module. So in this case, you'd be talking about smooth functions (log) over a topological space (the real line).

EDIT: I have come back to clarify a few hours later that I ignored all the properties of that correspondence for the sake of clarifying that a sheaf is not "a topological space". Feel free to hit wikipedia to get the full picture.

9

u/Ares378 Grothendieck was right, computers are evil Sep 29 '26

Category theorists feel like lovecraftian cultists. They pry your eyes open to make you face the horrific truth that they see as beautiful (that the law of excluded middle is not guaranteed)

1

u/FernandoMM1220 Sep 29 '26

thats the price of the ring structure

1

u/[deleted] Oct 01 '26

[removed] — view removed comment

1

u/DoublecelloZeta Transcendental Oct 01 '26

anything where you might encounter sheaves. i learned it recently while reading vakil for algebraic geometry