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

learn more… | top users | synonyms (2)

1
vote
1answer
28 views

Terminology of “G over H”

I am trying to find the definition of G/H (which is read as "G over H", "G modulo H", or "G mod H"). I believe that, in this case, G is a group and H is a subgroup of G.
2
votes
2answers
33 views

Name for introducing negation with quantifiers

The rewriting of $\varphi\to \psi$ into the logically equivalent $\neg \psi\to\neg \varphi$ is called contraposition. Is there a similar word for rewriting $\forall x.\varphi$ into $\neg\exists ...
1
vote
0answers
24 views

Operator for scaling a function?

Let $\mathbb{F}$ denote the set of functions of the form $f: \mathbb{R} \to \mathbb{R}$. I am interested to know whether there exists a well-known linear map $T_\alpha: \mathbb{F} \to \mathbb{F}$ ...
1
vote
0answers
25 views

Partially ordered sets

I have a question on Posets. Suppose we have $P = \{3, 6, 9, 18, 7, 14\} $ ordered by divisibility. We want to partition $P$ to subsets so that each two elements in each subset are related directly ...
6
votes
3answers
1k views

Difference between “space” and “mathematical structure”?

I am trying to understand the difference between a "space" and a "mathematical structure". I have found the following definition for mathematical structure: A mathematical structure is a set (or ...
5
votes
2answers
444 views

Difference between “space” and “algebraic structure”

What is the difference between a "space" and an "algebraic structure"? For example, metric spaces and vector spaces are both spaces and algebraic structures. Is a group a space? Is a manifold a space ...
1
vote
0answers
21 views

On the Name of the Amplituhedron

Shouldn't the 'amplituhedron' really be called an 'amplitutope' since it's really a polytope and not strictly a polyhedron?
0
votes
3answers
2k views

What do these terms mean: commutative, associative, distributive

I am reading a book, and I am trying to understand what the writer really mean by the following terms. I would like to understand what these words mean in relation to the examples. In regular ...
0
votes
0answers
14 views

A Geometry Terminology Question

Edges and diagonals are to polygons as faces and X are to polyhedrons? What is the answer to X? I've been touching up on geometry and I'm having trouble finding an answer to this, and inconsistency ...
4
votes
0answers
50 views

Can we consider a hypergeometric function as a closed-form?

Let's say a calculus problem like an integral or a series has a solution that inevitably involving a hypergeometric function. It turns out that hypergeometric function cannot be expressed in term of ...
5
votes
6answers
565 views

Problem in the second-derivative symbol.

The second derivative of this symbol according to the rules that we have learned the correct mathematical, I wish to know why this symbol is not used.
0
votes
1answer
25 views

Term for functions with infinite derivatives [closed]

Functions that include a negative indice such as x-1 or similar have an unlimited number of derivatives, so f'(x), f''(x), and fn(x) exist. Is there a technical term for functions like these? I've ...
0
votes
1answer
20 views

Validity of the term 'cost' in 'cost function'

I am studying machine learning and came across the term "cost function." Although I understand the basic idea, I am wondering how the term applies to specific problems (i.e., finding the cost of a ...
2
votes
0answers
59 views
+50

Have any authors suggested mathematics-wide prefixes for “missing a quotient” and/or “missing an identity”?

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation." seminorm pseudometric Similarly, the prefixes in the following terms both mean: ...
0
votes
0answers
10 views

Are there terminologies distinguishing modules over ring and rng?

Let $R$ be rng. Let $M$ be a left $R$-module. Let's say, after some verification, one realized that $R$ has a unity and it doesn't satisfy $1_R \cdot x$ for all $x\in M$. Hence, one cannot call $M$ ...
0
votes
0answers
9 views

Is there a name for products $\Delta(v)\!\cdot\!M$ and $M\!\cdot\!\Delta(w)$?

For any vector $u$, define $\Delta(u)$ as the diagonal matrix whose diagonal elements correspond to the entries in $u$. Now, let $M$ be an $m \times n$ matrix, and $v$ and $w$ be $m$- and ...
1
vote
1answer
34 views

What properties does a rank one matrix have?

My question is what properties does a rank one matrix have? I saw a lot of papers mentioning that the matrix is rank one and so on. I know rank one of a matrix means that there are no independent ...
0
votes
1answer
27 views

Bigger and Smaller for numbers - Works in both directions?

I wanted to know how to use the right term when explaining the difference between numbers. For example, I have two lenses: Lens 1 = 10x zoom Lens 2 = 5x zoom I know I can say that the 1 has 2x ...
1
vote
0answers
17 views

The name of $fusc$ (Calkin-Wilf sequence)

I was just wondering where $fusc$ got its name (where $fusc(2n) = fusc(n), fusc(2n + 1) = fusc(n) + fusc(n + 1)$, seeds: $fusc(0) = 0, fusc(1) = 1$). The function is of some importance in the ...
2
votes
2answers
15 views

Origin of the words arithmetic and geometric progression

Why are arithmetic progression and geometric progression called arithmetic and geometric respectively?
3
votes
2answers
34 views

Is there are term for location plus orientation, without magnitude?

Is there a concise, accepted term for a piece of information that describes location (translation from origin) plus orientation (angular position / attitude), but ignoring magnitude? In a little ...
-4
votes
1answer
61 views

What Do We Call a Conjecture When It Is Proved? [closed]

When Legendre's conjecture is proved, what will its new name be? I have researched this and I think law or theorem might be used, but I want to know for sure. Legendre's law of prime numbers between ...
0
votes
0answers
14 views

Financial math vocab; “convertible”, “roll over”?

I am having trouble understanding what is going on regarding the following problem. Smith receives income from his investments in yen. He finds a bank that will issue a term deposit that allows ...
6
votes
1answer
255 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 ...
0
votes
2answers
84 views

Spivak “min” notation confusion

Spivak uses a notation: min$(1, \frac{\epsilon}{2|a| + 1})$ What does he mean by this notation? especially by "min"??
0
votes
0answers
14 views

Nomenclature for posets s.t. for all $x<y$, there exists $z$ with $x<z<y$.

I can't remember the nomenclature (if it exists) for a poset with the property in the title, that is, a poset $(P,\leq)$ with the following property: If $x<y$ in $P$, then there exists $z\in P$ ...
1
vote
1answer
35 views

What do “canonical” and “natural” mean exactly?

"Canonical" and "natural" are two words frequently seen in mathematical literature. For example, we often find "there is no canonical/natural way to", "it's canonical/natural to". So I'd like to know ...
1
vote
1answer
38 views

One Half of a Primorial

Is there a name for a half primorial? How should a half primorial be notated? The first three primorials are 2,6, and 30. The first three half primorials are 1,3, and 15. I have found that the half ...
0
votes
0answers
27 views

Usage of the term Q.E.F.

While researching the term Q.E.D last night, the phrase Q.E.F was mentioned, which was apparently "used by Euclid to indicate the end of the justification of a construction". Does Q.E.F indicate the ...
0
votes
0answers
11 views

Term of partially ordered set with “levels”

Suppose that we have a partially ordered set $(X,\leq)$ such that the following condition holds: There exists a disjoint partition $X = \bigcup_{ i \in \mathbb N_0 } X_i$ such that for $i < j$ we ...
6
votes
0answers
55 views

Name of a certain set

I want to know if there is any already-standard way to refer to the set described as follows. Take the set of all primes in $\mathbb{Z}$, call it $\mathbb{P}$. Take the set of all finite products of ...
2
votes
2answers
233 views

What are the names in English for Alterando, Invertendo, Componendo and Dividendo?

I am writing an article in English but don't want to use the Latin names. What are their English equivalent?
1
vote
1answer
53 views

Definition of a binary operation is the same as definition of a closed binary operation?

I'm reading Wikipedia about operations and binary operations . Intuitively I always thought that a binary operation is a operation that takes two arguments. But Wikipedia defines a binary operation as ...
0
votes
1answer
16 views

The Value of One Function Determines the Value of Another

The value of $\pi(s)$ determines the value of $m(n)$. How do we describe such a relationship between two functions in standard terminology? How do we express this mathematically?
5
votes
2answers
185 views

Two point topological space

Is there a standard name for the two point space with precisely one singleton being the only nontrivial open set? What are its most noteworthy categorical properties?
0
votes
0answers
44 views

Products of All Primes Up To The $n$th Prime

The first prime is 2. The second prime is 3. 3·2=6. The product of the first three primes is 30. The product of all the primes up to the fourth prime is 210. My question is this: Is this sequence ...
1
vote
0answers
36 views

Is there accepted terminology for algebraic structures whose every subalgebra is free?

Is there accepted terminology for algebraic structures whose every subalgebra is free? Examples: Any free group Any vector space More generally, any free module over a PID. In fact, this ...
2
votes
0answers
32 views

Does the phrase '$S$ is independent' have an accepted meaning in universal algebra?

Let: $T$ denote an algebraic theory $F$ denote the free functor $X$ denote a $T$-algebra. $\mathrm{cl}_X : \mathcal{P}(X) \rightarrow \mathcal{P}(X)$ denote the function such that for all $S ...
0
votes
1answer
16 views

Which operations create a minor of a graph?

I came across two definitions which operations are allowed to construct a minor from a given graph. One definition allows edge contractions and edge deletions, the other additionally vertex ...
0
votes
0answers
25 views

Soft question: Distribution of the kth powers of normal random variables.

If $X_1,..,X_n$ are standard normal random variables then it is knows that: $\underset{i=1}{\overset{n}{\sum}} X_i$ is a normal random vairable and $\underset{i=1}{\overset{n}{\sum}} X_i^2$ is a ...
0
votes
0answers
29 views

Definition For Bound

Let $a$ be any natural number and $b$ be the next prime greater than $a$. Let $m$ be the maximum distance from $a$ to $b$ such that $a+m$ is equal to or greater than $b$. Can I call $m$ the bound? ...
2
votes
2answers
41 views

Sequence vs Series

What is the difference between a sequence and a series and how should they be used i.e. give examples of the usage of these terminologies in separate senarios.
0
votes
1answer
18 views

Formula For Finding the Next Near Consecutive Perfect Square

For any three consecutive members of a sequence, the first and third members are near consecutive. 1 squared is 1. 2 squared is 4. So 1 and 4 are consecutive perfect squares. 1 squared is 1. 3 ...
0
votes
1answer
34 views

What's the name for this writing of a polynomial of degree 2?

Going from $$2 x^2 + 12 x + 25$$ to the form (1) $$2(x+3)^2+7$$ is called "mise sous forme canonique du polynôme du second degré" in French, but it seems (I looked in various sources) that the ...
0
votes
1answer
16 views

Bounded by a constant?

What exactly is meant by "constant" when it is said that Legendre's conjecture implies that the upper bound on the prime gap above n could be bounded by the product of a constant and the square root ...
0
votes
0answers
9 views

Near Consecutive - Assistance With Terminology

Examples: 1 and 2 are consecutive. 1 and 3 are not, but they are near consecutive. 89 and 97 are consecutive primes. 89 and 101 are not, but they are near consecutive primes, by which I mean they are ...
1
vote
0answers
35 views

term for a sum of diagonal and skew-symmetric matrix?

Is there a term for a matrix that is a sum of a diagonal and a skew-symmetric matrix? One particular example of this is a 2x2 matrix of the form $$ M = \begin{bmatrix} a & b \\ -b & a ...
2
votes
1answer
24 views

Terminology: what is the “generic character” of a ternary quadratic form?

The title says it all: What is the "generic character" of a ternary quadratic form? Motivation: I'm reading a really old paper, and the author refers to this terminology without any further ...
5
votes
1answer
80 views

What word means “the property of being holomorphic”?

As in the title, I am looking for a single word meaning "the property of being holomorphic". The obvious candidates are "holomorphy" and "holomorphicity" but both look wrong to my eye. ...
0
votes
2answers
24 views

Word Form of Big O Notation

O of (the contents of the parentheses) Is this the correct way to say an expression with big O notation in words, just as y=f(x) is read y equals f of x? The expression with the big O followed by ...