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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1answer
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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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Question on terminology for implications when consequent is always true.

The implication $X\rightarrow Y$ is referred to as being vacuously true when the antecedent is false (i.e., $X=\bot$). Is there similar terminology to be said when the consequent is true (i.e., $Y=\...
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Is $\sqrt[3]{x^3}$ monomial? [duplicate]

I have been confused by different interpretations of polynomial and monomial. Is $\sqrt[3]{x^3}$ really a monomial?
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Property of $f(x, y)= z$ for all permutations of $x, y, z$

What property would you say a function $f(x, y)= z$ has if it is true for all permutations of values $x, y, z$?
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Is there a common name for the shape described as a segment of a circle or ellipse?

A circular segment is a region of the area inside a circle partitioned from the rest of the circular area by a chord. Is there a common name for this shape, other than "circular segment"? If ...
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A standard name for an “inversely (uniformly) continuous” map

Is there a standard name for a map $f: X → Y$ between metric spaces such that for every $ε > 0$ there is $δ > 0$ such that $d(x, y) < δ$ if $d(f(x), f(y)) < ε$ for $x, y ∈ X$ and/or for a ...
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Symmetric vs Symmetrical

I was reading an engineering book. It says " A turbomachine with symmetrical velocity triangles...". I personally felt more naturally right away to say symmetric velocity triangles. What is ...
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Composite vs Composition: which one is the correct word?

So, I am a bit confused about the word I should use to refer to $$f\circ g.$$ I have always used ''composition'' but I have seen some people (perhaps everyone who uses the term correctly) say ...
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What is meaning of term “ F is Algebraic Galois over K”

I am trying exercise questions in Field Theory from Algebra by thomas hungerford and there in some questions author asks about prove that " F is algebraic Galois over K". Now, I am not able ...
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Is the Phrase “Any Given $x \in \mathbb{Z}$” Okay to Use in a Math Article? [closed]

I wonder whether the phrase "any given" as it appears in the title above is ambiguous.
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$k$th-order Taylor polynomials rules in English / US math education

In France, an important topic for undergraduates in analysis is what is called Développements limités. The concept is based on $k$th-order Taylor polynomials. It uses a series of rules like: The $k$...
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How to understand the convention on describing the “position” of mathematical objects

When studying algebra, I find that it seems like a convention that we use positional words like on, under, over etc. to describe relations between things. For example: $V$ is a vector space over $F$. ...
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What is the difference between a partition and a subinterval? [closed]

For example the norm of a partition is the widest subinterval
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Understanding Slope Better

Recently, I have realized how much I have taken for granted in understanding the slope of a line and the slope of a curve in general. With that said, I wanted to clear up my understanding to make sure ...
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How do constants differ from numbers?

Although I scanned the other version that's not Early Transcendentals, in Calculus Early Transcendentals 7th ed 2011, James Stewart never defines "constant". It first appears on p. 3 but not ...
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What do we call an exponential object in a concrete category that basically equals the one in Set

So suppose you've got a concrete category $\mathcal C$ and two objects $X, Y$ of $\mathcal C$. For instance, $\mathcal C$ could be the category of topological spaces and we could also suppose that $Y$ ...
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“… are not enough general” What does it mean?

Note: The concept $T_{\min}$ and $T_{\max}$ spaces are not enough general. $T_{\min}$ or $T_{\max}$ topological space $X$ will be either indiscrete space, or $\{X,A,\emptyset\}$ or $\{X,A,A^{c},\...
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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: \...
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Terminology to indicate functions convex in certain arguments

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....
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Is there a term for this concept involving functions? [duplicate]

If $f_1:X_1\to Y_1$, $\ldots$, $f_n:X_n\to Y_n$ are maps, is there a term for the map $\left(x_1,\ldots,x_n\right)\mapsto\left(f_1\left(x_1\right),\ldots,f_n\left(x_n\right)\right)$ from $X_1\times\...
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Modular Numbers: Not Accounting for Decimal Portion in Decimal Expansion

Let n = 10, s = 4. [s] = {s' $\in \mathbb{z}$ | s' $\sim$ s} = {s' $\in \mathbb{z}$ | 10 | s' - 4} = {10k+4 | k $\in \mathbb{z}$ } = {s' $\in \mathbb{z}$ | decimal expansion of s' ends in a 4 if s' is ...
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How do even and odd functions relate to even and odd numbers?

How do the notions of oddness and evenness apply to both functions and numbers? If Even and Odd functions share nothing in common with Even and Odd numbers, then why were Even and Odd adopted for ...
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Naming theorems proved by mathematicians sharing the same surname

Background It's a usual practice to use a mathematician's surname to name a result. The question Who decides after whom a theorem or conjecture is named? has given a description on how this "...
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A generic terminology for left and right parts - i.e. M and N - of a general lambda application term MN?

As pointed out in the comments, the rhs and lhs are both terms, so "rhs term" and "lhs term" works. There may be a more evocative, and equally concise term. Presumably (?) the only ...
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Does the overline in the expression functions as a vinculum or something else?

$a - [ a - \{ a - (a - \overline{{a - 1}})\}]$ If the overline functions as a vinculum, the value of this expression should be - $a + 1$ Is it correct? Could anybody please help me to understand ...
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Is there a symbol to indicate a fraction normalized to the unit interval [0 to 1]?

I'm looking for a symbol/character that quickly conveys to the reader that the number that follows is to be understood as a decimal fraction in the range from 0 (minimum) to 1 (maximum). So for ...
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Why is a “list” of values associated with a variable (e.g. X1, X2, … , Xn) often called variables (plural)?

One of the most common beginnings of any statistics or probability proofs goes something like: ...
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Is there a reason the word “collection” is used in Heine-Borel theorem to describe an open covering instead of “set”?

The Heine-Borel theorem is stated as follows: Suppose $\mathcal{H}$ is an open covering of a compact set $S \subseteq \mathbb{R}$. Then $S$ is of an open covering $\tilde{H}$ consisting of finitely ...
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Taking the limit on the first variable, or over the first variable, or?

I asked the following question on the English Usage page, and it made people furious why I didn't ask here. So I do: suppose $f(x,y)$ is a function of two variables and I want to say: "take the ...
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Mapping vs function [duplicate]

I am reading an engineering mathematics book whose author says that the term mapping and function have the same meaning and whether one calls $f:X\rightarrow Z$ a function or mapping is a matter of ...
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Concrete and abstract numbers

Recently I heard about the concepts of concrete number = numerus numeratus and abstract number = numerus numerans. See here. These seem to be mathematical-philosophical specialist terms of medevial (...
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Is Counting Regarded as Repeated Addition?

I am uncomfortable with the following statement in the draft of my paper: [T]he unary system of representing $n$ by $n$ contiguous dots uses a singleton alphabet and requires counting rather than ...
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What's the generalisation of right-continuous to non-handed spaces?

A function $f$ is right continuous at a point $c$ if it is defined on an interval $[c, d]$ lying to the right of $c$ and if $\lim_{x→c^+}f(x) =f(c)$. Moving deliberately into less precise language, I ...
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Name of factors in Gaussian Elimination

Consider something like $\begin{pmatrix}1&2\\ 3& 4\end{pmatrix}^{-1}$. The classical way to do this is to write it next to an identity matrix, like the following: $$\begin{pmatrix}1&2\\ 3&...
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Preimage of semi-infinite interval — terminology

For a function $f:\mathcal X \to \mathbb R$ and $L \in \mathbb R$, does the the preimage of the semi-infinite interval $$ f^{-1}(\infty, L] = \big\{x \in \mathcal X\,:\,f(x) \leq L\big\}$$ have a ...
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Can We Speak of the “Prime Factorizations” of the Positive Rationals?

I am of two minds with respect to this question; therefore I will lay out the case for the existence of prime factorizations of positive rationals such as $2.5$ or $\frac{22}{7}$, and then I will lay ...
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What is the term used for a “factorial” of prime numbers ? Is there such a definition?

A "factorial" of a given number $n$ is defined as a product of positive integers up to that number. What is the term used if those positive integers are prime numbers? Is there a term for ...

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