# Tagged Questions

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

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### $f$ attains its minimum, delta definition

I just want to check if the following "definition" makes sense and is correct: A function $f: X \rightarrow \mathbb{R}$ attains its minimum if $\exists \delta > 0$ such that $f(x) \geq \delta$, ...
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### Is there a definition that defines the set of all factors of a natural number? [closed]

So let's say that you have the number $n=12$. The factors of $12$ are $1$, $2$, $3$, $4$, $6$, and $12$. I'm wondering if there's some definition that when you plug in a natural number $n$, it will ...
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### Is every Closed set a Perfect set?

From 'baby' Rudin. I've seen that a set is closed iff it contains all of its limit points. In Rudin, $(d)$ says if every limit point of E is a point of E, then $E$ is closed. He also says $(h)$: $E$ ...
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### Prove Limit Addition Thm as x approaches infinity

I am supposed to prove prove $\lim_{x\to \infty} [f(x)+g(x)]= L+M$. Starting to realize I don't really understand the formal definition of a limit, although I do understand the general concept. ...
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### What does bounded in module mean?

I'm trying to understand Liouville's theorem and in the book I'm reading it's stated as Let $f$ be a holomorphic function on the complex plane, which is bounded in module in a neighborhood of infinity ...
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### Why is this first-order ODE considered non-linear?

Consider the following equation: $$y'=\sin y.$$ What causes this equation to be considered non-linear? $y'$ is not multiplied by a power, and neither is $\sin y$.
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### Why are matrix norms defined the way they are?

Given $A$ a square matrix Define: $\|A\|_1$ as the max absolute column sum $\|A\|_2$ as the sum of the squares of each element $\|A\|_\infty$ as the max absolute row sum Pray tell, why are ...
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### Contribution of a loop to the degree of a vertex in a graph

Prehistory I've recently started learning graph theory in my institute (as a part of discrete mathematics course). During a lecture the professor had given a definition for a local degree of a vertex ...
Is the following logical notation valid in describing the condition for a function $f$ being surjective? If $f: A \rightarrow B$ is a function, then $f$ is surjective if \forall y, \exists x \in A \...