Feb 4, 2023 · While in infinite dimensional spaces it may be infinite in cardinality, the sums $$ \Sigma_ {i=1}^n b_iv_i $$ , will be finite sums; sums over finite subsets of our infinite basis.

Why is the infinite sphere contractible? I know a proof from Hatcher p. 88, but I don't understand how this is possible. I really understand the statement and the proof, but in my imagination this...

Dec 10, 2023 · Here's a proof by induction that the resistance of a finite version of this ladder with $\ n\ $ rungs is indeed homogeneous of degree $1$ in the variable $\ R\ .$ Taking the limit as $\ …

Apr 10, 2013 · Has anyone read this article? This accomplished mathematician gives his opinion on why he doesn't think infinite sets exist, and claims that axioms are nonsense. I don't disagree with his …

An infinite number? Kind of, because I can keep going around infinitely. However, I never actually give away that sweet. This is why people say that 1 / 0 "tends to" infinity - we can't really use infinity as a …

Dec 1, 2014 · But the circumference also defines the subset with infinite area that lays "outside" (which is a conventional concept). That other "outside shape" would be an example of a finite-perimeter …

May 11, 2023 · Can you give me an example of infinite field of characteristic $p\\neq0$? Thanks.

Feb 22, 2016 · I using the definition - If a set is countably infinite, then each element of the set can be mapped to the set of natural numbers. Another question - Is the cardinal product of countably infinite …

Jul 13, 2024 · This was initially sparked by a hypothetical question: There are two scenarios. In the first, an infinite number of people are living in a completely blissful paradise, but every day a person is se...

Apr 13, 2022 · Infinite powers of matrices using the concept of generalized inverses. An introduction to interval matrices and a brief idea of why studying infinite powers for such matrices can help capture …