# Tagged Questions

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### Is calling a linear-equation a linear-function, misnomer or completely wrong?

From my college life, I remember many professors used to call a linear-equation a linear-function, however: A standard definition of linear function (or linear map) is: $$f(x+y)=f(x)+f(y),$$ ...
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### Why is a perfect group called a perfect group

A group is called perfect if we have $[G,G]=G$. I was wondering in what sense is this group perfect? I've never really done anything much with perfect groups so I don't really know anything about ...
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### The Jacobi nome $q$

Does anyone know why $q = e^{-\pi K'/K} = e^{\pi i \tau}$ is called the nome? Is there a historical reason? Does the word nome mean something in Latin or German?
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### Is there a specific term for such collections of filters?

Let $U$ be a set. Concept = "a set $\mathscr{C}$ of proper filters on $U$ such that if $X\in\mathscr{C}$ and $Y$ is a proper filter on $U$ and $Y\supseteq X$, then $Y\in\mathscr{C}$." Is there a ...
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### Why are left/right adjoint functors not called up/down?

I am studying category theory and I recently learned about adjoint pairs of functors. It seems to me that they are called left and right adjoints because if we have categories $\mathcal{C}$ and ...
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### Why do we want to define a $k$-scheme to be birational if the rational map (and its inverse) to $\Bbb A_k^n$ is over $k$?

Two varieties $X,Y$ are said to be birational if there exist rational maps in each direction such that either composition is the identity on a open dense subset. Note that here the morphisms aren't ...
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### Have arrows in a category with this property a special name?

Studying posets I encountered the notation $a\prec b$. It means that $a<b$ and no $c$ exists with $a<c<b$. If $a\prec b$ then in words $a$ is covered by $b$. Looking at a poset $P$ as a ...
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### Definition: Theorem, Lemma, Proposition, Conjecture and Principle etc.

Definition: Theorem, Lemma, Proposition, Corollary, Postulate, Statement, Fact, Observation, Expression, Fact, Property, Conjecture and Principle Most of the time a mathematical statement is ...
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### Growth Rate. A precise definition.

Recently I came across a problem (see statement below) growth rate . During my attempts to solve the exercise I concluded that I do not know the meaning of need backup growth rate when this rate is ...
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### Why are compact sets called “compact” in topology?

Given a topological space $X$ and a subset of it $S$, $S$ is compact iff for every open cover of $S$, there is a finite subcover of $S$. Just curiosity: I've done some search in Internet why compact ...
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### Adding together curves or shapes to approximate something more complex

I'm looking for proper terminology / references for the following sort of problem: Say we have some one-dimensional curve like $y = 10$ defined over the real valued domain $[0,1]$, and we ask, how ...
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### From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
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