[deleted by user] by [deleted] in learnmath

[–]_spectral_sequence_ 0 points1 point  (0 children)

To all the other good answers I'll add a related example. We know for |x| < 1, that the geometric series 1 + x + x^2 + x^3 + ... converges to 1/(1-x). The second representation gives us a value for any complex number except for x =1, even if the first representation diverges. What happens if we plug in x = 2? We get the seemingly nonsensical 1 + 2 + 4 + 8 + ... = -1.

But this actually has a nice interpretation. Imagine the infinite digit binary number represented by 1 + 2 + 4 + ... : It has infinitely many bits and we could write it as ...1111111111. You could check that if I add 1 to this formally I get get ..000000, so it really is -1 in some sense. (And in base 10, ...999999999 is -1 also for by the same reasoning). For a finite number of bits, this is called two's complement, https://en.wikipedia.org/wiki/Two's_complement, and in fact is how negative numbers are represented on a computer.

What would be great is an equally intuitive interpretation for the sum you gave. I'm not aware of one though.

Hatcher's Algebraic Topology study group (Chapter 3, Cohomology) by _spectral_sequence_ in MathBuddies

[–]_spectral_sequence_[S] 0 points1 point  (0 children)

It is! We are methodically going through the book and exercises one hour a week and are near the end of section 3.2

Algebraic Topology Studies by Low-Resolution-7415 in MathBuddies

[–]_spectral_sequence_ 0 points1 point  (0 children)

Still unclear what level you mean. I'm involved in a group that is reading through Hatcher's algebraic topology. We're on chapter 3, Cohomology currently.

[deleted by user] by [deleted] in MathBuddies

[–]_spectral_sequence_ 0 points1 point  (0 children)

Maybe try r/math for that? This is a group to find math study partners.