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 …

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 $\ …

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 …

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 …

You could just as easily argue that the sum of the distance is infinite so the distance will be infinitely far away. Both statements are paradoxes. But the concept of the limit of an infinite series being 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 …

Dec 27, 2018 · @foaly: "tensor product distributes over infinite direct products" is a question about the natural map being an isomorphism. Asking for there to be some arbitrary isomorphism is basically …

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.

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 ...

Dec 1, 2010 · Can you partition an infinite set, into an infinite number of infinite sets?