this post was submitted on 22 Jan 2024
126 points (100.0% liked)
Math Memes
1156 readers
1 users here now
Memes related to mathematics.
Rules:
1: Memes must be related to mathematics in some way.
2: No bigotry of any kind.
founded 1 year ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
Well, sets of measure 0 are one of the fundamentals of the whole integration theory, so it is always wise to pay particular attention to their behaviour under certain transformations. The whole 1 + int + int^2 + ... series intuitively really seems to work as an inverse of 1 - int over a special subspace of R^R functions, I think a good choice would be a space of polynomials over e^x and X (to leave no ambiguity: R[X, e^X]). It is all we need to prove this theorem, and these operators behave much more predictably in it. It would be nice to find a formal definition for the convergence of the series, but I can't think of any metric that would scratch that itch.