# Questions tagged [terminology]

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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### Is there a name for “point to set distance” when you vary the distance?

Recall: let $X$ be a metric space with metric $d$. Let $x\in X$ and let $A$ be a subset of $X$ and define $$d(x,A)=\inf\{d(x,a)\mid a\in A\}.$$ This $d$ on the LHS is called a just point-to-set ...
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### Is $n = 0$ in proofs involving mathematical induction a rigorous expression?

I have had this confusion from high school. In proofs involving mathematical induction, we always say for $n = 0$, blablabla, so that a certain condition holds for $n = 0$. After I learned logic, I ...
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### Number of balls touching one ball at the center.

Let $B$ be a ball of radius one in $\mathbb{R}^d$. I'm looking for references about the following problem : How many disjoint balls $B_i$ of radius one is it possible to put in contact (tangential ...
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### What is the term for simple (non-matrix) math?

Is there a term for "simple" arithmetic where all variables in the expression contain only single/scalar values and thus produce a scalar result? This is opposed to matrix math where a ...
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### Term for repeated exponentiation?

Is there a term (or operation) for repeated exponentiation? I.e. Repeated addition is multiplication, repeated multiplication is exponentiation, repeated exponentiation is X? Is there even such a term ...
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### Name of a certain set of vectors

Let $v,u\in V$, a normed vector space (or I guess a normed magma if we want to be general), and let $l=(l_1,\dots,l_n)$ be a list of positive lengths. Then what do you call the set of "chains&...
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### Is there a name for function $f(x)=\max(a, \min(x, b))$, where $a \leq b$?

Is there a name for function $f(x)=\max(a, \min(x, b))$, where $a \leq b$? What actually this function does: it keeps value in bounds of $[a, b]$.
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### Why are some functions called 'forms'?

The question is simple: why are some functions called 'forms'? Modular 'forms', bilinear 'forms', differential 'forms', quadratic 'forms', and so forth. It is not concretely a mathematical question ...
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### Is the length of a line a property of that line, or is it its own mathematical object?

I'm trying to understand the nature of mathematical objects. As far as I understand it, mathematics studies these objects. Geometric shapes are one kind of such object, including 1D shapes, namely ...
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### Confusions with Symbol “=” in Mathematics

I am having this question because of the axiom of equality: \begin{equation} \forall x \forall y \left(x = y \longrightarrow \forall z\left(z \in x \longleftrightarrow z \in y\right)\right). \end{...
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### Ideal of a group

The ideal is defined in the ring theory; In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements In the answer to this question What is the exponent of a ...
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### Does a mathematical definition have necessary and sufficient condition hidden in it? [duplicate]

Let us assume the following definition:  S is said to be A if S satisfies the condition C. '' -----------(P) Can it mean that:  S is A if and only if S satisfies the condition C. '' ---------- (...
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### Find the relationship between $x$ and $y$ so that $y:=0\rightarrow\frac{\pi}{2}\Leftrightarrow x:=y\rightarrow\frac{\pi}{2}.$

Find the relationship between $x$ and $y$ so that $y:=0\rightarrow \dfrac{\pi}{2}\Leftrightarrow x:=y\rightarrow \dfrac{\pi}{2}.$ I'm having trouble solving the multivariable calculus if I change the ...
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### Confusion on the definition of an indexed family of sets

Ive recently been learning set theory and a bit of topology and im very confused on the definition of an indexed family. Why do we say a family of sets instead of a collection of sets? And why is the ...
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### Name of the theorem for substituting integer arithmetic with modular arithmetic modulo all primes

The following proposition (which I consider true) allows to substitute (1) the congruence relation in modular arithmetic modulo all prime numbers with (2) the equality relation in integer arithmetic: \...
What's the appropriate terminology to indicate functions convex only in certain arguments? For example, consider the following function. $f: X \times Y \rightarrow \mathbb{R}$, $f(x, \cdot)$ is convex....