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

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1answer
103 views

Definition of “totient”

I had always taken the term "totient" to be defined by saying that the totient of a positive integer $n$ is the number of positive integers less than $n$ that are coprime to $n$. Thus, for example, ...
1
vote
1answer
102 views

Is there a standard name for this probability-theoretic construction?

What follows is a description of a concept in probability theory that I find very useful, but cannot find described in the literature. I've been calling it the "perplectic sum", but that's a term I ...
5
votes
3answers
185 views

Does “monotonic sequence” always mean “a sequence of real numbers”

When we say a sequence is monotonic, does that imply the sequence is Real Number Sequence? And other propositions about monotonic, all real-valued? When I see some ...
2
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1answer
91 views

A few basic questions about the arithmetical hierarchy, mostly about terminology.

I was reading about the arithmetical hierarchy, and I have a few questions, mostly notational. For completeness, here's the definition given over at Wikipedia. The classifications $\Sigma_n$ and ...
2
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3answers
69 views

Notation for definition and equivalence

I would like some clarification about the usage/meaning of $:=$ and $\equiv$. I have been using $A := B$ to denote "Let $A$ be defined as $B$." This is akin to assignment ...
12
votes
3answers
228 views

Why “integralis” over “summatorius”?

It is written that Johann Bernoulli suggested to Leibniz that he (Leibniz) change the name of his calculus from "calculus summatorius" to "calculus integralis", but I cannot find their correspondence ...
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0answers
63 views

Term for a number that when added to another number equals 1

Is there a term for the relationship between some number and a number added to it that makes it equal one? i.e. x + y = 1, thus y is the ____ of x. In the case I'm looking at, the numbers are the ...
0
votes
1answer
67 views

What is a set function that returns another set of points called?

I have a set of points $S = \{x_i\}_{i = 1}^m, x_i \in \mathbb{R}^n \forall i$. Now, I have a set function $f$ which operates as follows: $$f(S) = GX^T$$ where $G \in \{0,1\}^{m\times m}$ and $X = ...
2
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1answer
98 views

What is a “nonzero equation”?

Does it mean that there is at least one non-zero coefficient? That the solution set does not include the zero vector? That the the equation is non-homogenous? I am asking because the phrase is used ...
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1answer
30 views

Is there any rules for choosing letters about $a,b, c$ and $t$, or $2t$

we know:ellipse is the locus of dynamic point whose distances from two fixed points’ sum is fixed value. so I write: $z$ is complex number, and $a,b,c,t$ are reals. $$\begin{align*}\left| ...
0
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2answers
114 views

“Ordinary” and “polar” vector fields in Euclidean $3$-space

In his book Differential Forms with Applications to the Physical Sciences, on pages 19--20, Harley Flanders writes: "a one-form $$ \omega = P\,dx+Q\,dy+R\,dz$$ may be identified with an ...
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2answers
417 views

The origin/use of “derivative” and “differentiate”

Apologies if there is a duplicate somewhere; I couldn't find one. The use of the root "deriv" in the context of differentiation seems odd: we have differentiation, differentials, differentiable, ...
0
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1answer
64 views

Usually, main results are called theorems, while smaller results are called propositions. Is there a name for super-immediate results?

In mathematical papers, main results are called theorems, while less central results are called propositions. But sometimes, there is a result that is so immediate, it doesn't even deserve to be ...
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1answer
119 views

A name for set of disjoint intervals

What's in a name? That which we call a rose by any other name would smell as sweet. William Shakespeare I'm looking for a short name for the phenomenon collection of disjoint intervals. I ...
0
votes
1answer
87 views

What is the proper terminology for these two types of multiplication?

((QUESTION REWORKED)) First question on this site, and I apologize if this question has been answered. I searched and searched and the fact I don't know the basic terminology is hindering me from ...
6
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4answers
389 views

Different meanings of math terms in different countries

Does anyone know of a list of math terms that have (slightly) different meanings in different countries? For example, "positive" could mean $\geq 0 $ in some places, and "strictly positive" means ...
6
votes
3answers
173 views

Unambiguous terminology for domains, ranges, sources and targets.

Given a correspondence $f : X \rightarrow Y$ (which may or may not be a function) I generally use the following terminology. $X$ is the source of $f$ $Y$ is the target $\{x \in X \mid \exists y \in ...
0
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1answer
91 views

Is there a collective term for theorems, lemmas, properties, corollaries? [closed]

I wonder whether there exists a collective term for theorems, lemmas, properties and corollaries?
0
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1answer
80 views

Name for Cartesian Product variant that does not return an empty set if one of the sets is empty

I am looking for the name of this mathematical operation that behaves very similar to Cartesian Product. Given: A = {1,2} ...
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vote
1answer
29 views

What is a Linear Set of Points.

According to the classroom notes "Uniformly Continuous Linear Set" in American Mathematical Monthly, Vol. 62. No. 8(Oct., 1955) pp. 579-580, Author: Norman Levine He let E denotes a Linear Set of ...
5
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4answers
152 views

“Fixed $k$” in Mathematical Induction

On page 34, in his Calculus book, Apostol gives the following description of proof by induction: Method of proof by induction. Let $A(n)$ by an assertion involving an integer $n$. We conclude that ...
2
votes
2answers
89 views

What is the notation of 'a single term in the DFT'

I have a notation/terminology question: I am writing a paper in not-quite-my-area and can't figure out the right way to phrase/notate the following: I have a discrete function $p[x]$, of which I can ...
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1answer
33 views

Signatures and L-Structures

Consider the field of real numbers $\mathbb{R}$. This is an $L$-structure. Is there such a thing as an $S$-structure (i.e. a signature structure)? Or because we can recover a first order language from ...
2
votes
2answers
552 views

What are the two 'sides' of a decimal number called?

Is there a fancy name for the "left side" and "right side" of a decimal number? (That is, the pre-decimal part and the post-decimal part.)
4
votes
1answer
37 views

How to denote an 'atomic' morphism in category?

I want to distinguish between two disjoint classes of morphisms in a category: (1) those morphisms that are composed of other morphisms (other than identities) and could conceivably be factored into a ...
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3answers
1k views

What is a fraction in which the greatest common factor of the numerator and the denominator is 1?

What is this fraction: A fraction in which the greatest common factor of the numerator and the denominator is 1?
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2answers
107 views

Are “prime factorization” and “integer factorization” the same?

Are "prime factorization" and "integer factorization" the same? If not, what is the difference?
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3answers
246 views

When does it make sense to say that something is almost infinite?

I remember hearing someone say "almost infinite" on one of the science-esque youtube channels. I can't remember which video exactly, but if I do, I'll include it for reference. As someone who hasn't ...
2
votes
1answer
122 views

Zech's logarithms - Why are they called “Zech”?

Zech's logarithms are defined in here. I couldn't find a reason why they are called "Zech". The only thing a dictionary suggests is that Zech is an abbreviation for Zechariah, which doesn't seem ...
2
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3answers
62 views

Name for $X^\infty=\bigcup\limits_{k=0}^\infty X^k$

I'm making structures associated with groups, rings and so on in OCaml and in order to do so I started by defining sets and a few operations (intersection, union, difference, carthesian product, ...
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3answers
2k views

What does “isomorphic” mean in linear algebra?

My professor keeps mentioning the word "isomorphic" in class, but has yet to define it... I've asked him and his response is that something that is isomorphic to something else means that they have ...
2
votes
3answers
1k views

Claim vs statement vs proposition

In logic, it seems like the words claim, statement and proposition have the same meaning: A sentence which can be true or false (but not both). I'm not sure if this is correct. Isn't there any ...
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4answers
97 views

Is the mathematical concept of an “operation” necessarily deterministic?

Does the mathematical concept of an operation require that the process is deterministic? If not, what are some example cases for non-deterministic operations? Motivation: I am coming from a ...
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0answers
42 views

Decisive equivalence of collections of probability measures

Working on the optimal decision theory in stochastic setting, I've found out that the following notion of equivalence is very useful. Let $(X,\mathscr A)$ be a measurable space, and let $\mathrm ...
0
votes
1answer
32 views

What is the difference between “model” and “method”

I am not sure which forum to ask this question since the answer may change depending on the scientific area. I am analysing some time series using linear regression. I predict data using the linear ...
1
vote
1answer
42 views

Is there a name for the following asymmetry property of a measure on $R$?:

Let $\mu$ be a Borel measure on $\mathbb{R}$. I am looking for a name for the following property: $\int_\mathbb{R} f d\mu \ge 0$ for all skew-symmetric Borel functions $f$ that are non-negative on ...
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votes
3answers
1k views

“IFF” (if and only if) vs. “TFAE” (the following are equivalent)

If $P$ and $Q$ are statements, $P \iff Q$ and The following are equivalent: $(\text{i}) \ P$ $(\text{ii}) \ Q$ Is there a difference between the two? I ask because formulations ...
1
vote
1answer
95 views

What is a finite partial function from $\mathfrak c$ to $D=\{0,1\}$

While I reading a paper, there is a notation is called finite partial function. I searched by google, I cannot find its definition. So I post it here as a question: What is a finite partial ...
3
votes
2answers
110 views

Who did first use the term “simple” in group sense and why?

Who did first use the term "simple" in group sense? More appreciated if I learn the original word(might be in French, Galois???)... and also... Why do you think that this term is chosen ...
3
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0answers
84 views

Phrase and symbol for “geometric absolute value”$ e^{|\ln(x)|}?$

I'm calculate the median fractional difference between two vectors (to characterise the error in a quantity with a high dynamic range). If $a/b = 0.1$, the fractional difference is $10$, and if $a/b ...
3
votes
3answers
308 views

What is a rational trigonometric function? Is $\cos x$ rational?

I am reading Trigonometry by Gelfand and Saul. On p.140 they discuss rational trigonometric functions and define one as: A rational trigonometric function is a function you can get by taking the ...
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2answers
82 views

What does “unconfirmed or conditional” mean on this site?

On the home page of the “Bounded gaps between primes” polymath project, there are listed bounds for $H$ in Zhang's proof of prime gaps. For example: What does “unconfirmed or conditional” mean ...
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0answers
74 views

Is there a standard name for the relation $X \times Y$?

Given sets $X$ and $Y$, is there a standard name for the relation $f : X \rightarrow Y$ whose graph equals $X \times Y$? Something like the full/maximum/top/total/complete relation?
2
votes
2answers
115 views

What does it mean to “identify” points of a topological space?

I was recently reading about circle rotations (a basic example in dynamical systems) and got confused by some notation. It said consider the unit circle $S^{1} = [0,1]/{\sim}$, where $\sim$ indicates ...
2
votes
2answers
103 views

The union of a countable set of countable sets?

Let $A$ be an countable set, and let $B_n$ be the set of all $n$-tuples $\left(a_1,\ldots,a_n\right)$ $B_n$ is the union of a countable set of countable sets. This question maybe about the ...
2
votes
1answer
51 views

Name for a certain class of groups that contains all the abelian groups

I cam across this type of groups. Is there a name for groups that satisfy this condition: $$\forall x,y\in G[xyx^{-1}\in \langle y\rangle]$$ As mentioned in the title, it is easy to see that all the ...
2
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0answers
21 views

A question about terminology of repeating functions

Imagine some experimental data is repeating in $\left(0,T \right) , (\Delta t,\quad T+\Delta t) , \left( 2\Delta t,\quad T+2\Delta t \right), ... $. I can not say the data is periodic since $\Delta ...
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0answers
225 views

Is the kernel of any ring homomorphism a subring, according to this definition?

This is an exercise taken verbatim from Birkhoff and MacLane, A Survey of Modern Algebra: Show that if $\phi: R \rightarrow R'$ is any homomorphism of rings, then the set $K$ of those elements in ...
4
votes
1answer
78 views

Ideal:Kernel :: Filter:?

I understand that the notion of a filter is in some sense dual to the notion of an ideal, at least in the context of Boolean algebras1. Let $f:{\mathbf A} \to {\mathbf B}$ be a Boolean algebra ...
0
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1answer
48 views

Formal notation when using the axiom of specification

The axiom of specification states formally that for every property $\varphi$ holds $\forall X\exists Y\forall x(x\in Y\longleftrightarrow x\in X\wedge\varphi(x))$. Since from the axiom of ...