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

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8
votes
2answers
400 views

What is an element of a rng called which is not the product of any elements?

Let $R$ be a non-unital ring. Let $F:R\times R\longrightarrow R$ be a function given by the formula $F(x,y)=xy.$ Let $r\not\in\operatorname{im}(F).$ Such elements can exists, for example $2\in 2\...
4
votes
1answer
4k views

Base ten is called “decimal”; what's the name of numbers in base 15?

Good afternoon all, I was wondering is there a table of names for the base x of numbers? For example, I know that numbers in base 10 are called "decimal", those in base 2 are called "binary", base 16 ...
1
vote
1answer
128 views

terminology: euler form and trigonometric form

Am I right, that the following is the so-called trigonometric form of the complex number $c \in \mathbb{C}$? $|c| \cdot (\cos \alpha + \mathbf{i} \sin \alpha)$ And the following is the Euler form of ...
2
votes
1answer
85 views

Other Names for Sierpinski Reals / Leaning Tower of L'viv

There is a poset constructed by combining in a certain way the usual order on the reals with any well-order on the reals (I can provide details if needed). I've heard it called the "Sierpinski Reals" ...
0
votes
2answers
104 views

What is this called? (Equations involving percentages)

I am trying to describe our formulas to our users, and have forgotten the basic math term for these 2 types. First one is: $$y=x+10\% $$ $$z=y+10\%$$ if $x$ was $10$, then $z$ would be $12.1$. Other ...
0
votes
1answer
44 views

Two terminology question about relations

Is there a name for constructing a set from a relation (or, more generally speaking, from a set of pairs that are tuples)? For example, let $R = \{(0, 1), (1, 2), (2, 3)\}$; if you collect all the ...
1
vote
0answers
86 views

What are variables with fractional powers called?

What are variables with fractional powers ( e.g. $x^{\frac{3}{4}}$) called in contrast to monomials for positive integer powers?
1
vote
1answer
194 views

What is an honest basis?

In a comment to this question, the commentator stated that "the monomials form an honest basis for your vector space". To be honest, I never heard of that. Is this something elementary?
0
votes
3answers
293 views

What do I call a unit vector parallel to a coordinate axis?

What do I call an arbitrary element of this set of vectors? $$ \begin{align*} \{&\langle 1, 0, 0 \rangle, \\ &\langle 0, 1, 0 \rangle, \\ &\langle 0, 0, 1 \rangle, \\ &\langle -...
6
votes
2answers
3k views

Generalization of variance to random vectors

Let $X$ be a random variable. Then its variance (dispersion) is defined as $D(X)=E((X-E(X))^2)$. As I understand it, this is supposed to be a measure of how far off from the average we should expect ...
1
vote
1answer
34 views

Range mapping process name

Does the process of mapping a random range, for example, [4; 55] to [0; 1] have a name? Maybe it's called normalization?
0
votes
2answers
323 views

How does mathematical coefficients differ from “physical coefficients”?

In the Talk page of Wikipedia Coefficient I read this comment: As far as I can tell, the mathematical definition should imply that coefficients are unitless, however, the physical sciences have ...
64
votes
5answers
4k views

Why “characteristic zero” and not “infinite characteristic”?

The characteristic of a ring (with unity, say) is the smallest positive number $n$ such that $$\underbrace{1 + 1 + \cdots + 1}_{n \text{ times}} = 0,$$ provided such an $n$ exists. Otherwise, we ...
3
votes
1answer
124 views

A poset that's the union of the lower sets

Let $(P,\leq)$ be a poset, and let $\downarrow\! p = \{ x\leq p\}\subseteq P$. Let $M\subseteq P$ be the subset of all maximal elements of $P$. Question: is there a specific term for a poset $(P,\...
3
votes
1answer
233 views

What's the correct name for a geometric solid that's a beanbag?

enter image description hereMy daughter is in the first grade, and I'm having a good deal of fun trying to determine the shapes of irregular geometric solids. I'm stuck on the good, old beanbag. ...
1
vote
1answer
158 views

Using two or more “such that”.

I'm wondering if it's right (and not abusive or ugly) the use of two, or more, "such that" in a definition, and in the dealing with mathematical objects. I know that I could find equivalences for such ...
6
votes
1answer
2k views

Function theory: codomain and image, difference between them

Can't figure out the difference between them. I have read wiki article about codomains and images, but what is the difference? It seems confusing the examples part in codomain article. How can we ...
3
votes
0answers
194 views

Constructing a semigroup from a small category

The following was given as an example for a semigroup without an identity: Finite sets of matrices of varying dimensions, where the product $A*B=\{PQ \mid P \in A, Q \in B \text{ and } dim(Q)=...
5
votes
3answers
560 views

Generic Elements of a Set.

Mild Motivation: In writing a post about the Baire Category Theorem, I learned the neat fact that a "generic" $f\in C^{0}([a,b], {\mathbb R})$ was nowhere differentiable and not monotone on any ...
0
votes
1answer
161 views

Is topological perimeter not defined anywhere in the literature?

I don’t understand why I have never seen topological perimeter defined anywhere in the literature. Is it not a useful/interesting notion? Let’s consider the following example. Suppose that $M$ is the ...
3
votes
3answers
280 views

Is there a name encompassing both limit inferior and limit superior

Is there a mathematical term which would include both liminf and limsup? (In a similar way we talk about extrema to describe both maxima and minima?) The only thing I was able to find was that some ...
3
votes
1answer
5k views

Relationships among the terms “slope”, “parameter”, and “coefficient”?

In $y=mx$, is $m$, are there different implications of referring to $m$ as a "slope", a "coefficient", a "parameter"? Or perhaps the "slope coefficient" or "slope parameter"? For context, I am ...
1
vote
2answers
1k views

Is there actually a difference when we say 'perpendicular' vs 'tangent'

I find myself often getting these two words mixed up a lot. So let's say I have a simple graph of $y = t^2$ and $x = t$. If a line is tangent to the curve at the origin, it would only be the line y =...
3
votes
2answers
119 views

What's the most concise way to refer to this shape?

What would you call this shape? Not the shape in green, I mean the entire object.
3
votes
3answers
4k views

Definition of “maximal” and “minimal” [duplicate]

Possible Duplicate: difference between maximal element and greatest element When I first encountered the terms maximal and minimal, I confused them with maximum and minimum. Many of my ...
-1
votes
3answers
111 views

Is there a name for this type of groups?

A group having more than one elements with only one element as inverse of each element in the group. Is there any name for that? Let me explain my question: $(\{0\}, +)$ is a trivial group with ...
28
votes
7answers
17k views

Is there any difference between mapping and function?

I wonder if there is any difference between mapping and a function. Somebody told me that the only difference is that mapping can be from any set to any set, but function must be from $\mathbb R$ to $\...
4
votes
3answers
199 views

Does this generalisation of Latin squares have a name?

I am interested in looking at $n\times n$ tableaux (or matrices) in which (WLOG) each integer in $\{ 1, 2, \ldots, n \}$ occurs exactly $n$ times. This is a generalisation of a Latin (or even semi-...
1
vote
2answers
155 views

Is $i\in n\Leftrightarrow i\in\{0,\ldots,n-1\}$ a common knowledge?

Is $i\in n\Leftrightarrow i\in\{0,\ldots,n-1\}$ for every $n\in\mathbb{N}$ a common knowledge? I am to publish a research article which uses this notation for convenience. The question: Should I ...
0
votes
3answers
4k 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 algebra,...
2
votes
0answers
57 views

terminology clarification needed: projection of a measure to an open set

I'm reading in Doobs "Classical Potential Theory and its Probabilistic Counterpart" and I'm having trouble with terminology. Specifically, in Part I chapter 6, he talks about the projection of a ...
1
vote
0answers
128 views

Is there a name for a number whose factors' exponents are all prime?

For instance, 864, whose factorization is 2^5 x 3^3.
11
votes
0answers
161 views

Why are parabolic subgroups called “parabolic” subgroups?

I used to think that things called "parabolic" must have something to do with parabolas or their defining quadratic equations. In fact, terms like parabolic coordinate, parabolic partial differential ...
15
votes
5answers
4k views

What do you call numbers such as $100, 200, 500, 1000, 10000, 50000$ as opposed to $370, 14, 4500, 59000$

There are different categories of numbers that we use every day. Integers that written in decimal notation have $1, 2$ or $5$ as the leading figure, followed by none, one or more zeros. These are ...
2
votes
3answers
138 views

Name for a bipartite graph in which one vertex set has maximal degree 1?

I'm looking for a specific name for a bipartite graph $(U,V,E)$ in which there is at most one edge incident to each vertex $u \in U$. That is, $|E_u| \le 1$ for all $u \in U$, where $E_u = \{(u,v) \in ...
4
votes
4answers
1k views

Name for “decimals” in other bases?

In grade school, numbers that use a positional notation along with a decimal point (to delimit integer and fractional parts of a number are called "decimals". This "point" notation is easily ...
5
votes
0answers
81 views

Terminology: functions on lattices

is there a name for the class of functions $f: L\times L \rightarrow L$, where $L$ is a lattice and $L\times L$ is the product lattice (ordered pointwise), with the following property: $f(x,y)=f( x \...
1
vote
0answers
122 views

When was the term 'ramification' first used in math literature?

In my studies so far, I have had the word 'ramification' come up in Algebraic Number Theory and Complex Analysis. The Wikipedia article tells me that 'ramification' is also used in some other fields. ...
1
vote
1answer
86 views

Terminology for properties of functions.

So I was wondering, is there a name for a function whose output is always less than or equal to its input ($f(x)≤x$)? I know there is a name for functions that satisfy $x_1<x_2\rightarrow f(x_1)<...
2
votes
4answers
132 views

“Down-Closed”, “Down Ideal”, Something Else?

Let $X$ be an a set and let $\mathcal{C}$ be a collection of subsets of $X$ satisfying the following property: If $A$ and $A^\prime$ are subsets of $X$ with $A \in \mathcal{C}$ and $A^\prime \...
6
votes
1answer
1k views

Isomorphism of sets

What is an isomorphism of sets? I know in general an isomorphism is a structure-preserving bijective map between two algebraic structures. But what algebraic structure does a set have? Does a ...
3
votes
0answers
237 views

Can GCD be called an operator?

Can $\gcd(a,b)$ be called a binary operator which takes operands $a$ and $b$ and returns their greatest common divisor. And if for some operator —say $\bigotimes$ —$(a_1\bigotimes a_2 \...
6
votes
3answers
501 views

Etymology of the word “isotropic”

Given a quadratic form $q : V \rightarrow k$, a nonzero vector $v \in V$ is said to be isotropic if $q(v) = 0$. Any subspace of $V$ containing such a vector is also said to be isotropic, and the ...
9
votes
3answers
606 views

Does *finitely many* include the option *none*?

Does finitely many include the option none? Say I have a sequence $(x_n)$ and I want to say that there can only be $0$ or $n\in \mathbb N$ non-zero terms. Can I say that the sequence has finitely ...
0
votes
1answer
90 views

Is there a name for a set of numbers that equally surround another number?

This has to do with web page pagination, let's say there are a lot of pages (e.g. 100) and you're on page 35 and the pagination links at the bottom of the page show: prev | 32 | 33 | 34 | 35 | 36 | ...
4
votes
3answers
188 views

What's the name for the equivalence induced by a function on its domain?

Any function $f$ with domain $X$ induces an equivalence relation on $X$, with classes $$\{f^{-1}(\{y\})\,:\, y \in \operatorname{im}f\;\} .$$ Is there a name for this equivalence? Thanks!
1
vote
1answer
634 views

What does Linear Congruential mean?

How does one interpret the terms "Linear" and "Congruential" as in a "Linear congruential RNG"? I am used to linearity by $f(ax)=af(x)$. This does not seem to me to hold true in this case ($\bmod$). ...
1
vote
1answer
596 views

What is a word to describe curves that have a tangent but are curved away from each other?

I'm writing a description that involves two curves behaving (approximately) as shown below. There aren't actually two intersections: they are mutually tangential. Also, I have many such curves, this ...
2
votes
1answer
254 views

What is the origin of the (nearly obsolete) term “binary decimal”?

What is the origin of the (nearly obsolete) term "binary decimal"? At least two important publications in the 1930s used this oxymoron to mean what is now ...
1
vote
2answers
207 views

Modifying a discrete probability distribution according to set of weights

Given a discrete probability distribution (e.g., ${P_1=0.85,P_2=0.05,P_3=0.05,P_4=0.05}$), I would like to transform it according to some set of "weights" (say, ${w_1=2,w_2=0.5,w_3=1,w_4=0.5}$), which ...