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 …

Oct 4, 2020 · I am a little confused about how a cyclic group can be infinite. To provide an example, look at $\\langle 1\\rangle$ under the binary operation of addition. You can never make any negative …

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 $\ …

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 …

Jan 31, 2025 · There are the following textbooks to learn about infinite-dimensional manifolds: "The Convenient Setting of Global Analysis" by Andreas Kriegl and Peter W. Michor

Write out a few terms of the series. You should see a pattern! But first consider the finite series: $$\sum\limits_ {n=1}^ {m}\left (\frac {1} {n}-\frac {1} {n+1 ...

The dual space of an infinite-dimensional vector space is always strictly larger than the original space, so no to both questions. This was discussed on MO but I can't find the thread.

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 …

Jan 26, 2021 · I would like to have some examples of infinite dimensional vector spaces that help me to break my habit of thinking of $\\mathbb{R}^n$ when thinking about vector spaces.