It is just what you want it to be, as long as it makes sense mathematically. We can talk about $+\infty$ and $-\infty$ in the extended real line, and about $\infty$ in the extended comlex plane. We can talk …

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 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 $\ …

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 …

Jan 23, 2022 · This means that for infinite entropy we can't have differentiable self-maps of compact manifolds or Lipschitz self-maps of compact metric spaces of finite lower box dimension. The …

Mar 23, 2021 · So if you want to prove "Every infinite set of natural numbers admits a surjection from $\mathbb {N}$ " without using the axiom of choice, you need to at some point use something …

Dec 15, 2025 · Can a countable set contain uncountably many infinite subsets such that the intersection of any two such distinct subsets is finite?

Sep 10, 2019 · Your further question in the comments, whether a vector space over $\mathbb {Q}$ is finite dimensional if and only if the set of vectors is countable, has a negative answer. If the vector …

May 31, 2014 · Infinite dimensional clifford algebras are the setting of David Hestenes' so-called "universal geometric algebra". Hestenes uses this setting to embed vector manifolds---manifolds …

Apr 4, 2014 · The Lipschitz condition is verified for pairs of points, and any pair of points lies on a line — thus, the infinite-dimensionality of the space does not really come into the picture.