# Questions tagged [definition]

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

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### what $H^1_q$ is?

I don't know the meaning of the notation $H^1_q$ (a Sobolev space)? Where I can find the exact definition of that notation? Thank you in advance.
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### What does “smallest” mean in this definition?

In first-order logic, a set $\tau$ of terms is the smallest set of strings (finite sequences of symbols) over the sets of variables, constants, and function symbols such that: Any variable is a term. ...
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### Is the root of a number defined as a single number or a collection of numbers?

I always had trouble understanding one thing about roots: Imagine that we want to find the solutions for the following equation: $$x^2 = 4$$ It's easy to see that the solutions are $2$ and $-2$. But ...
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### Why are there no cycles of length 2?

A graph $G$ is an ordered pair $(V,E)$ of disjoint sets where $$E\subset V^{\underline{2}}:=\left\{\{x,y\}\ |\ x,y\in V\land x\ne y\right\}.$$ Let $G=(V,E)$ be a graph. A path $P$ in $G$ is an ...
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