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Questions tagged [terminology]

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

Terminology is a discipline that studies, among other things, the development of terms and their interrelationships. This tag is intended to be used for questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

8534 questions
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What does it mean "arbitrary but fixed" in a proof?

I've read related questions but I couldn't find a clear explanation as to, for example, when one should use "...an arbitrary but fixed...". Does it mean that my variable has a certain property so it's not any variable? but most importantly, When…
user923938
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What is the correct meaning of term "formula"?

What is the correct meaning of term "formula"? My teacher says that a formula is valid for all values of variables we plug in. Is it true that we can say formula is valid for all defined values of variable we plug in? I got this doubt when he told…
Lalit Tolani
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Equivalent to 'Minimum' meaning 'Closest to zero'?

If we refer to the Minimum of a set of numbers, we mean the lowest number. Min(12, 7, 18) = 7 and Min(5, -8) = -8. Is there a technical term for the 'number closest to zero'? e.g. where fn(5, -8) = 5 and fn(-5, 8) = -5 Similarly, what would be the…
HappyDog
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name for difference between sum of upper half and lower half of a set.

Given a finite set of numbers $X =\{1, 2, 3, 4, 5\}$, define the upper half $U = \{4, 5\}$, and the lower half $L = \{1, 2\}$ (We omit $3$/median here if there are odd number of elements in $X$). So $L,U$ is not strictly a partition of $X$. There…
peng yu
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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 $[a, b]$.
æ-ra-code
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Are $x^y$ and $x^z$ "Powers" of $x$?

Or would "powers of $x$" in those examples refer to $y$ and $z$, respectively?
JustAsking
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What do we mean when we say that $x \in \mathbb R$

When we say that $x \in \mathbb R$ does here $x$ represents all real numbers at the same time or $x$ represents only a single real number at one time. How can a single variable($x$) represent all the real numbers at the same time ? when we write $x…
Shashwat singh
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What's the English term for this algebra operation?

I didn't study maths in English so apologies for this trivial question. How do you say in English when you have a formula 3n + 3 and you want someone to convert it into 3(n+1) I only know about "rearrange" but that's usually about equality, like…
Daniel Katz
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What is difference between Reduction, Simplification, and Cancellation?

I know basics, concepts and an idea of these terms. I am mathematician myself. However, I'm struggling to understand the precise semantics of these English terms, and what exactly they imply in the Mathematics. So, what is an exact, semantically…
Giorgi Tsiklauri
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Difference between "is closed under" and "is stable under"?

In https://en.wikipedia.org/wiki/Bornological_space it is said that A bornology on a set X is a collection ℬ of subsets of X such that [...] ℬ is stable under inclusions, i.e. if A ∈ ℬ and A′ ⊆ A, then A′ ∈ ℬ; where "is stable under" sounds very…
Make42
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How exactly do you read the logic of an equation such as this..

I'm a computer science-type, and trying to get a deeper grip of "math-speak." The use of the equal sign is not clear to me in terms of when it's being used as "assignment" vs. "equality." Where $y=x$, it's intuitive that as $x$ varies over…
Jordan Fine
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Does the mathematician use the prefix “non” always strictly mean “not necessarily”?

I came across https://books.google.com/books/about/Mathematical_Writing.html?id=wpQvBQAAQBAJ Where it talks abt the difference of non and not Sounds like mathematician use non to mean “not necessarily” or “not definitely” Where as “not” means…
Kim Stacks
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What is the origin of the term/concept "pagoda function"?

In the classic book Winning Ways for Your Mathematical Plays, volume 4, 2nd edition, p. 818, Berlekamp, Conway and Guy write about the use of pagoda functions to study peg solitaire like games. The authors observe: pagoda functions are known to few.…
Humberto José Bortolossi
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'Intuitive' relations: does this have a name?

Every now and then you run into some literature where the author has not managed to completely formalize their ideas, but they have provided some notion of how the quantities in question relate. Case in point: Birkhoff's aesthetic measure: $$ M\;…
Peter
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What does double bars mean in KL Divergence?

I did a google search and only things that pop up are parallel lines or norms, both I don't think makes sense in this context: https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence How do you interpret D(P || Q)?
confused
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