# Tagged Questions

For requesting, clarifying, and comparing definitions of mathematical terms.

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### What is a separable closure? And why the standard definition of algebraic closure is defind as so?

Instead of defining it as a subfield of algebraic closure, what would be the natural way to define it? Here's what I figured out: Let $F$ be a field and $E$ be an extension field of $F$. ...
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### Intuition behind independence & conditional probability

This is a basic question. I have a good intuition that $A$ is independent of $B$ if $P(A \vert B) = P(A)$, and see how you can easily derive from this that it must hold that $P(A,B) = P(A)P(B)$. ...
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### On definition and usefulness of “Cayley table”

Dummit-foote p.21 Let $G=\{g_1,\cdots,g_n\}$ be a finite group with $g_1=1$. The Cayley table of $G$ is the $n\times n$ matrix whose (i,j)-entry is $g_ig_j$. This definition is based on an ...
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### What is a point?

In geometry, what is a point? I have seen Euclid's definition and definitions in some text books. Nowhere have I found a complete notion. And then I made a definition out from everything that I know ...
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### Injective or one-to-one? What is the difference?

What is the difference between the terms 'injective' and 'one-to-one', 'surjective' and 'onto', and 'bijective' and 'isomorphic'?
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### Mathematical structures with name reffering to a country

I am looking for a list of mathematical structures (not theorems) that refer to a country or nationality. I only know of Polish spaces and Polish groups. Does anyone have other examples? Note: many ...
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### Is there an intuitive, not-too-mathematical way of thinking about limit points? [duplicate]

so I know this question has been asked sooo many times. But I just have a few questions in particular, which despite searching, I haven't found an answer to. I appreciate any help. Book's definition: ...
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### Comparing Open Bases and Covers

In Topology, I see a resemblance and similarity between open bases and open covers. Although this is a short question, what is the defining difference between the two that sets them apart? ...
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### What is the definition of a finite set $S$? [closed]

This question is intended mainly for beginners. We can say "$S$ is not infinite" or "counting elements of $S$ is a procedure that (theoretically) terminates", a little of maths appears in “$S$ is ...
### Meaning of the term $X/H$ and orbits
I am trying to find representations of the group $G=GL_2(F(t)/t^2) = (M_2(F_p) , + ) \rtimes GL_n(F)$ So I was trying to do exactly what Serre has explained in this section. I am not quite able to ...
Definition 1. Let $R$ be a ring with invariant basis number and $M$ be a free $R$-module. Then, the rank of $M$ is the cardinality of an $R$-basis of $M$. ${}$ Definition 2. Let \$...