Let $X$ be a topological space. Call $x,y\in X$ swappable if there is a homeomorphism $\phi\colon X\to X$ with $\phi(x)=y$. This defines an equivalence re...

I've seen identities, which means they have infinite solutions.$\longleftarrow$This is incorrect; see the comments below. Examples are$$4x+6=2(2x+3)$...

I feel like different sources use the term "rank" differently, which is perhaps leading to my confusion. When I think of rank I think of number of linearl...

I am trying to find the limit of the sequence by using root test and I don't understand why the limit is not zero? (the answer is inf).

Let $G=(\mathbb C^*,\cdot), G'=(\mathbb R^*,\cdot)$ and $\phi : G\to G'$ be defined by $\phi(z)=|z|, z\in \mathbf C^*$, where $\mathbf C^*=\math...

this is something that came up when working with one of my students today and it has been bothering me since. It is more of a maths question than a pedago...

Factor $x^4+1$ over $\mathbb{R}$ Well, I read this question first wrongly, because the reader is about complex analysis, I did it for $\mathbb{C}$ first. ...

Can you help me identify the name of the algorithm described here that calculates the check digit of a $10-$digit number? Given a $012\text-345678\text-n$...

I was given the assignment to find a proof for the following $$A, A\rightarrow B, C\rightarrow\lnot B\models\lnot C$$ I understand that when all the hypot...

I have the following problem in which I have to apply both the chain rule and the FTC 1. I got the right answer, but i'm confused about what's r...