/sci/ - Science & Math

>>11444095
Deliberations as follows:
[math]K_0 (S) = K_0 (S^+ , S)[/math]. Strong excision gives [math]K_0 ( S^+ , S) \cong K_0 (B(H), S)[/math].
So, way I look at it, you need to show that every equivalence class in [math]K_0 (B(H))[/math] has a matrix representative in [math]K_0 (S(H))[/math]. Honestly, if the class of the matrix with the identity in the first entry does, you're golden, but it's also pretty likely to be a counterexample for [math]H[/math] infinite dimensional.

Also, compact projections are always finite. Just reminding you.

Also try to mess around with actions of [math]M_n (S)[/math] on [math]H^n[/math]. I think [math]M_n(S)[/math] ends up inside the algebra of compact operators in [math]H^n[/math], which should facilitate computations.

>>11370755
We have a set S.
Choosing some of them means that you have a function [math]f : S \rightarrow \{0, 1 \} [/math] , where we'll say that if [math]f(x)=1[/math] then x was chosen, and otherwise it wasn't.
There are 2^n of these functions, and we subtract the case of no element being chosen.
>>11371253
Sounds normal.
>>11371743
Depends.
>>11371798
[math]x_i y_i x_j y_j = x_j y_j x_i y_i[/math].
>>11372151
Please don't post such depressing things.

>>11362449
Here you go gigachad, my best joke recommendations.
https://link.springer.com/book/10.1007/978-3-030-33143-6
https://link.springer.com/book/10.1007/3-540-28890-2