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

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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 ...
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0answers
22 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 ...
6
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0answers
82 views

Name of a certain set

I want to know if there is any already-standard way to refer to the sets described as follows. For a set $X$, let $-X = \{-x: x \in X \}$; call it the negative of $X$. Take the set of all primes in ...
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1answer
17 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?
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0answers
46 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 ...
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0answers
37 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 ...
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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 ...
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1answer
19 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 ...
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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? ...
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2answers
46 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.
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1answer
22 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 ...
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1answer
36 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 ...
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1answer
17 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 ...
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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 ...
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0answers
32 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 ...
2
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1answer
30 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 ...
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2answers
39 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 ...
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1answer
91 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. ...
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0answers
11 views

Looking for name of function for the indexing of one ordering relative to another

If $A$ and $B$ are two orderings of the same (distinct) $k$ elements, there is a unique "index sequence" $P$ such that $A[P]$ is equal to $B$. For example, if $A$ and $B$ are $$ \begin{align*} A ...
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2answers
36 views

Meaning of a commuting maps?

What is commuting and commuting maps in mathematics? Did they different with commutative group?
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0answers
38 views

Mathematics and dyslexia, about left and right cosets and ideals

How often I had to run for help at Wikipedia each time I was confused about right cosets, or left ideals. So I devised a trick that would avoid to constantly being confused. In the definition of left ...
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2answers
317 views

Definition of factor - Is n a factor of n?

Is there a universally agreed upon definition of what a factor of a number is? Is $n$ a factor of $n$? Is $1$ a factor of $n$? EDIT x 2: Integers Natural Numbers
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0answers
32 views

Is there a conventional symbol for the set of real algebraic numbers?

The real numbers are denoted ℝ, and the algebraic numbers are conventionally denoted 𝔸. Is there such convention for the real algebraic numbers ℝ∩𝔸?
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2answers
85 views

In $\mathbb{R}$ does finite mean bounded?

I am looking over a exercise that states "Prove that if I is a closed, bounded interval which is contained in the union of some collection of open intervals, then I is contained in the union of some ...
4
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3answers
76 views

What is the meaning of percentile?

I am confused by the term percentile. Once my teacher told me that percentile means the percentage with respect to the score of the highest achiever. This means that if in a competition I got $80$ ...
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1answer
48 views

Venn diagram for a relation

My high school math book says the following diagram is a Venn diagram. But I think this is not correct. Is it right? If not, what is the following diagram that represents a relationship called?
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2answers
49 views

Is there a name for the function that gives me the signal of a number only?

I know the function that gives the absolute value of a number is called either absolute function or 'modulus' function, such as: $$ modulus(-6) = modulus(6) = 6 $$ Now, I want to name a function that ...
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1answer
23 views

Terminology — lying over something

I just came across reading something like this: 'Let $\phi\in \text{Gal}(L/K)$ lie above $Frob\in \text{Gal}(K^{un}/K)$.' Where $Frob$ is the Frobenius automorphism and $K^{un}$ is the maximal ...
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2answers
197 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?
3
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1answer
27 views

Terminology - Limit doesn't exist

Take the following limit: $$ \lim_{x \to 2} \dfrac{x+2}{x-2} $$ This doesn't exist. My textbook says it doesn't because "The denominator approaches 0 (from both sides) while the numerator does not." ...
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0answers
30 views

What is the difference between perturbation theory and numerical analysis?

What is the difference between perturbation theory and numerical analysis? Both subjects are trying to obtain the approximate answer. What are they study specifically?
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0answers
21 views

Order on the set of partitions (terminology)

Let $S$ and $T$ be partitions of some set $U$. What is the name for the partition $\{ X\cap Y \mid X\in S, Y\in T, X\cap Y\ne\emptyset \}$? Should it be called the infimum of $S$ and $T$? meet of ...
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2answers
42 views

Name for shape defined by volume between two concentric spheres

Is there a proper name for a shape defined by the volume between two concentric spheres? My understanding is that, formally, a "sphere" is strictly a 2D surface and there's a formal term for volume ...
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5answers
99 views

Why the term “countable”?

In my computer science theory class, we are discussing the concept of countability. I understand the concept, but the choice to use the word countability seems absolutely unintuitive to me. Why was ...
3
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0answers
45 views

A variant of projective objects?

Let $\mathcal{C}$ be an additive category. Is there a common name for objects $P \in \mathcal{C}$ with the property that $\hom(P,-) : \mathcal{C} \to \mathsf{Ab}$ is right exact, i.e. preserves all ...
3
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1answer
89 views

Is “connected, simply connected” Redundant?

Here are my definitions of "connected" and "simply connected." A topological space $X$ is connected if and only if it is not the union of two nonempty disjoint open sets. A topological space ...
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4answers
142 views

How do you read the symbol “$\in$”?

A variable in an equation may be replaced by any of the numbers in its domain. The resulting equation may be either true or false. Here is another way to show ...
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0answers
32 views

What's the mathematical name to scale a number to a new resolution

From a programmers background, i know what i need to accomplish, and how i should, but i don't know if there's a mathematical name for what i'm doing here... For examle, i have the number 5 in a ...
2
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2answers
56 views

Does the word 'ten' have a base?

My friends and I had a debate: "Does the word 'ten' have a base?" My Argument: 'ten' is only 10 in base 10 so if i have 10 objects, counting in base 10, when I get to the end of the list, I will ...
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1answer
51 views

Maximum/Maximal set

Maximum or maximal set with property $P$ When I was reading some textbooks, I noticed that I do not get the meaning of the following two phrases. ($P1$) $\quad$ maximum set with property $P$ ($P2$) ...
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1answer
59 views

How would you describe category $\mathsf{Rel}$?

I encountered two definitions for a category denoted by $\mathsf{Rel}$: Objects are pairs $\left(A,R\right)$ where $A$ is a set and $R$ a relation on $A$. Arrows in ...
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0answers
12 views

Name of the set of points equidistant from a line

I was reading about geometrical shapes in n-dimensional Euclidean spaces and programming some objects that would share some of their properties in different dimensions, like n-spheres. I had somewhere ...
6
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1answer
478 views

What does “s.t.” mean?

English is my second language and I have a question. What does "s.t." mean? $ \text{min} \quad f(x) = (x1−2)^2+(x2−1)^2 $ $ \text{s.t.}\qquad g_{1}(x) = x_{1} - 2x_{2} + 1 = 0 $ $ \qquad\qquad ...
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5answers
75 views

In probability: is there a name for 1-x or x-1?

I should frame this question in the context of dealing with probabilities: I've read the wikipedia entry on the multiplicative inverse: http://en.wikipedia.org/wiki/Multiplicative_inverse Where it ...
0
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1answer
29 views

Is there any special name for a $n$-torus made by products of hyperspheres?

I was wondering if there exist an accepted name for an $n$-torus made by the product of hyperspheres $\mathbb{S}^d$, that is for the following set: $$ ...
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1answer
46 views

What does it mean “sequence with infinite range”

I'm trying to understand this phrase Find a sequence with infinite range that converges only to $0$. What does it mean "sequence with infinite range"? Thanks
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0answers
9 views

Terminology for particular situations?

What might be the name for a situation where a Hermitian (complex) operator produces real values? Could it be inversion, or convolution or something of that sort? And can the reverse situation be ...
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2answers
27 views

Terminology - variant of a hypergraph

In a hypergraph, we have vertices $V$ and hyperedges $H$, where each hyperedge is a subset of $V$. Suppose that we would like the hyperedges to be (ordered) tuples, rather than subsets. Does this ...
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1answer
25 views

Does a graph of this type have a name?

Does a graph of this type have a name? When I say a "graph of this type" I mean where the scales on the axes aren't uniform all the way along.
2
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1answer
41 views

Is algebra over a set also algebra over a field?

During my studies I have come across two different notions of the term "algebra", namely algebra over a set and algebra over a field (the field its vector space always being Euclidean space in my ...