Tagged Questions

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

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-2
votes
0answers
30 views

Why is a linear order called linear?

Why does the definition of linearly ordered set imply that we can make a diagram of this set as a line in which a < b if and only if a is to the left of b?
1
vote
1answer
34 views

Is there a name for a function such that $f=e^g$?

Let $X$ be a topological space. Let $f:X\rightarrow \mathbb{C}\setminus\{0\}$ be a continuous function. Is there a terminology to call functions $f$ such that $f=e^g$ for some continuous map ...
6
votes
1answer
64 views

Why are models in logic called models?

A model is an interpretation of a given formal language under which any wff in a given set of wffs of this formal language is true. Why are models called models? What's the reasoning behind the name? ...
0
votes
0answers
19 views

Compact hypersurface in $\mathbb{R}^n$

Let $S$ be an $(n-1)$ dimensional hypersurface in $\mathbb{R}^n$. If we say that $S$ is compact, does this necessarily mean that $S$ has no boundary? Eg. $S$ can be a sphere but not a sphere cut in ...
0
votes
2answers
14 views

What is the Term for the Center of Mass Equation Structure

What is the term for the generic structure of this form of equation: SUM(Mi * Xi) / SUM (Xi) It is the same as the center of mass calculation.
0
votes
0answers
22 views

What is a Serre presentation of a Lie algebra?

For example, as in: Give a Serre presentation of Lie algebra $\frak{g}$ of type $G_{2}$. Is it the presentation in terms of Chevalley generators, which satisfy Serre relations?
2
votes
0answers
29 views

What's a concise word for “the expression inside a limit”? Limitand?

In $\sqrt {f}$, $f$ is the radicand. In $\sum g_i$, $g_2$ is a summand. In $x \times y \times z$, $y$ is a multiplicand. In: $$\displaystyle \lim_{n \to +\infty} h_n(x)$$ or: $$h(x) \to \ell \quad ...
2
votes
1answer
58 views

If $R = \frac{P}{Q}$ is a rational function, does $f(R) := \deg (P) - \deg (Q)$ have a traditional name/notation?

Suppose $R : C \subseteq R \rightarrow \mathbb{R}$ is a (univariate) rational function. Write $R=P/Q,$ where $P$ and $Q$ are polynomial functions $\mathbb{R} \rightarrow \mathbb{R}$. Is there a ...
1
vote
0answers
13 views

trail vs path in Graph Theory v/s Graphical Models

In my course on probabilistic graphical models, I learnt (quoting from page 36 of the book Probabilistic Graphical Models: Principles and Techniques by the same author) Path: We say that X1 , . . . ...
2
votes
0answers
30 views

Synonyms for “Theorem”

Some mathematical results, despite being formally proven, are not actually called "theorem". Examples include: Bertrand's postulate Pigeonhole principle Law of large numbers Do these names imply ...
3
votes
1answer
39 views

Variation on neighbourhood base

Suppose $\{\mathscr B(x) \mid x \in X\}$ is a collection of filters (or filter bases) on a set X, with each $x \in \cap\mathscr B(x)$. Then $$\mathscr T = \{U \subseteq X \mid (\forall x \in ...
1
vote
0answers
56 views

Does this lemma have a name or where can I find a proof?

Does the lemma at the bottom of this page have a name? Or could someone give me an idea of where I can find a proof? In case you can't access the link: Lemma $\ \ $ If $g$ is of class ...
7
votes
5answers
349 views

difference between nonpositive and negative numbers?

I am wondering if there is any difference between non-positive and negative numbers? I think that negative numbers mean "negative real numbers" and "Non-positive numbers" are negative real numbers ...
1
vote
1answer
48 views

What is a natural exact sequence?

I know what an exact sequence is, but I have searched for the definition of a natural exact sequence, and could not find it. Does "natural" perhaps mean some sort of preservation of structure? I ...
-3
votes
1answer
31 views

Difference of 2 numbers [closed]

My question: Can the difference of 2 real numbers A and B, be negative? For example: A = 2, B = 4. Is the difference between A and B -2 or 2?
0
votes
0answers
24 views

Term for Multiple Functions that Share Critical Points?

Is there a term for when multiple functions share each other's critical points? Or, in general, when one function has a subset of the critical points of another?
0
votes
3answers
49 views

Is there a concept that describes the relationship between A and B where one is a subset of the other?

I feel like there must be a name for this. What is the relationship between A and B called if (A⊆B or A⊋B) is true?
2
votes
0answers
30 views

Why is the nuclear norm called so?

A simple question. Why is the sum of the singular values of a matrix called its nuclear norm? What is the origin of, and motivation for, this term? Apparently the term nucleus is sometimes used to ...
0
votes
0answers
52 views

What is the name of $\bigcap_{x\in G} xHx^{-1}$?

Let $G$ be a group and $H$ be a subgroup of $G$. What is the name of $\bigcap_{x\in G} xHx^{-1}$? I remember that there was a special name for this set but I forgot..
0
votes
1answer
18 views

Need help with finding if a function has a name.

I watched a first year senior year class in China and saw a function on the board. $$ H^n_x = x(x+1)(x+2)\cdots (x+n-1)$$ you can see a similar problem here in Chinese. I think this function ...
2
votes
2answers
48 views

What to call the relationship $\frac 1x + \frac1y = 1$

I've rediscovered the fun of geometry recently and found the beautiful and (to me at least) unexpected result that the two diagonal lengths of a regular unit heptagon are related by: $$\frac1a + ...
1
vote
0answers
15 views

Function 'result arity'

Given a map from $m$-tuples to $n$-tuples, $m$ can be referred to as the 'arity' of the mapping. What's the terminology for $n$? I feel like this should be brain-dead easy to find but my ...
1
vote
0answers
22 views

Is there terminology of the form “$n$-something form” that generalizes quadratic form and cubic forms?

By definition, a quadratic form is a homogeneous polynomial of degree $2$, and a cubic form is a homogeneous polynomial of degree $3$. Is there accepted terminology, like $n$-ic form, $n$-atic form, ...
3
votes
3answers
123 views

Is “=” an Operator?

I know that $+$, $-$, $\times$, and $/$ are all operators. But is $=$ an operator? For example, in the equation: $5 \times 5 = 25$ I know $\times$ is an operator, but is $=$?
7
votes
0answers
48 views

Is “slightly deform” a well defined concept in mathematical proof?

In topological proofs the phrase "slightly deform" is widely used. To me, although I can accept the idea intuitively, the phrase "slightly deform" does not sound like a strict mathematical concept. ...
2
votes
2answers
26 views

Origin of the term `quermassintegral'.

What is the origin of the term `quermassintegral'? I think this is a german word. What would be its literal translation in English? The definition of quermassintegrals from wikipedia: Let ...
1
vote
1answer
25 views

What is the name of logic which considers several distinct undefined objects?

Here is an example of a sentence of set theory written in first-order logic $\forall w_1\forall w_2\forall w_3\forall x \exists ! y\text{ } \phi(x,w_1,w_2,w_3)$ (where $\phi$ is a definable ...
0
votes
0answers
9 views

Specific name of a scale from -10 to 10?

I am trying to refer to a scale from -10 to 10 with 0 being the center. Does this type of scale have a specific name?
10
votes
0answers
100 views

How to name these “ideals”?

Background. Let $\mathcal{C}$ be a symmetric monoidal category with unit $\mathbf{1}$. A subobject of $\mathbf{1}$ is just a monomorphism $I \to \mathbf{1}$. We may also call this an ideal of ...
0
votes
1answer
28 views

what is the name of the sum of all numbers inside a number, including the number itself?

ex.: 1+2+3+4+5+6+7+8+9+10=55 this it what I mean by "numbers inside "10", including "10" ...I was in bed, thinking of a quick way to calculate that, but with a way bigger number ( ex.: ...
0
votes
0answers
12 views

Equivalence class of functions that imply the same ordinal relations

Often we define functions only to succinctly describe an ordinal relation. For example, economists define a utility function such as: $$u(x,y)=xy$$ to imply that the point (2,5) is better than the ...
1
vote
1answer
92 views
+50

Equivalence relation over groups $a\asymp_sb :\rightarrow\exists n\in\Bbb Z:as^n=b$: terminology and decision problem

Let's define this relation over the elements of a group $(G,\cdot,e)$ $$a\asymp_sb :\rightarrow\exists n\in\Bbb Z(as^n=b)$$ where $a^n$ is defined as follow 1)$a^0=e$ 2)$a^{n+1}=aa^n$ Qestion ...
0
votes
0answers
18 views

Matrices with Continuous Indices

The components of a matrix $A$ can be written as $a_{ij}$. In Quantum we're starting to talk about a generalization where the indices are not elements of $\Bbb N$, but are instead continuous. Our ...
45
votes
3answers
4k views

Do we have negative prime numbers?

Do we have negative prime numbers? $..., -7, -5, -3, -2, ...$
0
votes
1answer
24 views

Name for the set {Mv : |v| = 1}

Let $M$ be a matrix on a normed vector space. Is there a name for the set $\{Mv : |v| = 1\}$?
-1
votes
2answers
28 views

X and Y have the same cardinality if and only if bijection from X to Y? [duplicate]

My textbook says "Let X and Y be sets. We say X and Y have the same cardinality if there is a bijection f: X --> Y." I was wondering why the text does not say "if and only if." A bijection implies ...
0
votes
1answer
14 views

Codomain confusion

I'm confused about the codomain of a linear transformation. If we have a linear transformation which maps from $\mathbb{R}^n$ to $\mathbb{R}^m$ and the range of the linear transformation is only the ...
0
votes
0answers
26 views

Upto which number of vertices does every graph have a name?

I have heard of many families of graphs and also many famous graphs named after persons who intensively studied it. But I did not find a complete list with the names of the graphs to, lets say, ...
5
votes
2answers
66 views

Nuances of the word “proposition” (versus “theorem”) in mathematical writing

In mathematical writing, the word "Proposition" is often used to label lesser theorems. However, I tend to feel that there's a further difference in the way the words "Proposition" and "Theorem" are ...
1
vote
1answer
19 views

(Partial) symmetry order for matrices

Does there exists commonly used ( possible partial) orderings which would rank matrices as a function of their "degree of symmetry"? I am thinking one could for instance have $\succeq_{SYM}$ defined ...
1
vote
1answer
41 views

Does this notion of the “directed area” of a closed curve in $\mathbb R^3$ have a standard name?

Given an oriented surface $\Omega$ in $\mathbb R^3$, consider the quantity $\mathbf A(\Omega)=\int_\Omega\hat n\,\mathrm dA$. We may call this the "directed area" of the surface because, when $\Omega$ ...
1
vote
1answer
62 views

nice name for the image of multivariable function

Consider a differentiable function $f:D\subset\mathbb R^m\mapsto \mathbb R^n$ with $m\le n$. I know if $m=1$ then $f(D)$ is called by "path", if $m=2$ then $f(D)$ is called by "surface" and if $m=3$ ...
-2
votes
0answers
46 views

Why is the natural logarithm 'natural'? [duplicate]

Simple question: Why is it that the natural logarithm is called 'natural'?
3
votes
1answer
70 views

Multiple integral differential notation

When writing a multiple integral, I have noticed there is sometimes used a shorthand for writing the differential in the integral. For example in $\mathbb{R}^3$ instead of writing $\mathrm{d}x\ ...
2
votes
0answers
32 views

The meaning of “In general” in mathematics

What is the meaning of "in general" in mathematical texts? Does it mean usually or it means always or sometimes usually and sometimes always according to the text?
0
votes
1answer
16 views

How do you say that variable is randomly chosen with a random distribution for range [3, 42]?

This question is only about how to formulate something in English for a bachelor's thesis in computer science. I have a variable $x$ which is randomly initialized. It is chosen from a (continuous) ...
-1
votes
1answer
18 views

Monotonicity of a sequence of length 1 or 0

A sequence or list $a_i$ is said to be strictly monotonically increasing if for each pair of adjacent elements the successor is greater than its predecessor, or: $a_i < a_{i+1}$. But what if there ...
0
votes
0answers
6 views

What is the name of the function $s_p$?

Let $p$ be a prime. Define $s_p(n)\triangleq \max\{m\in\mathbb{N}:p^m|n\}$, for all $n\in \mathbb{Z}^+$. Is there a name for this arithmetic function $s_p$?
1
vote
1answer
43 views

How do expressions like “more than” and “is more than” have different meanings?

I've looked up in my present math book that expressions like (1) "less than" and "is less than" and (2) "more than" and "is more than" have different meanings. I saw that "less than" indicates ...
0
votes
1answer
16 views

How is a coordinate system called where values increase to the bottom instead to the top?

In some computer graphics libraries the coordinate system is almost like the "usual" cartesian coordinate system. The only difference is that the $y$ values increas to the bottom, not to the top. ...