# Tagged Questions

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### Are there official names for these functions?

$\newcommand{\sgn}{\operatorname{sgn}}$ Does anyone know if the simple function $$y(x)=x^2\sgn(x)$$ or alternately $$y(x)=x|x|$$ has any (official) name in mathematics or engineering? or ...
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When an algebraic structure is defined, it is often defined as a set $S$ "along with"/"together with"/"having" operations $\circ_1, \circ_2, \ldots, \circ_n$, and "denoted" by $(S, \circ_1, \circ_2, ... 4answers 120 views ### Are there two conventional definitions of “holomorphic”? In Walter Rudin's Real and Complex Analysis, second edition, on page 213, two definitions are stated. One of them says the derivative of$f$at$z_0$is$$f'(z_0)=\lim_{z\to ... 3answers 545 views ### What is a Neighborhood? Which of these definitions is more commonly used, and in which contexts? Fix a point$x\in (X, \tau)$. Then a neighborhood around a point$x$is: a set$N\ni x$and$N\in \tau$a set$N$with$x\in ...
We all know that $0!=1$, the degree of the zero polynomial equals $-\infty$, the interval$[a,a)=(a,a]=(a,a)=\emptyset$ ... and so on, are conventions in mathematics. So is a convention something that ...
I wonder whether the following concept has a name. Suppose you are given a commutative diagram $\mathcal C$, that we think of a small category where each hom-class (i.e. hom-set) consists of at most ...