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

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28
votes
5answers
11k views

What is the term for a factorial type operation, but with summation instead of products?

(Pardon if this seems a bit beginner, this is my first post in math - trying to improve my knowledge while tackling Project Euler problems) I'm aware of Sigma notation, but is there a function/name ...
3
votes
1answer
98 views

Name for this triangle centre

Given a triangle I draw circles around each vertex. I chose the radii of these circles so that they are all mutually tangent. There is only one way to do this. I extend these tangents. They concur at ...
1
vote
1answer
224 views

Name of the intersections of a ball with the octants?

The eight regions of space defined by the eight possible combinations of signs for $(+/- , +/-, +/-)$ for $x$, $y$, $z$ are called octants. Given a ball of radius 1 centered in the origin $(0, 0, ...
19
votes
5answers
10k views

Domain, Co-Domain & Range of a Function

I'm a little confused between the difference between the range & co-domain of a function. Are they not the same thing (i.e. all possible outputs of the function)?
2
votes
2answers
302 views

probability terminology for parameter in a Markov process

Suppose $$P(\text{feature present at time} \ t \ \text{and} \ t+\Delta t) = \beta^{2}+\beta(1-\beta) \exp(\Delta t/\tau)$$ where $\tau = 1/(\pi_{01}+\pi_{10})$. What is $\tau$?
0
votes
1answer
491 views

What is the sum of all pairwise products of a number's digits called?

I'm looking for something like this and I want to know how it's called; I'm pretty sure there is a term for it. I will show an example: Let's say we take the number 9876. ...
1
vote
0answers
104 views

Finite Levenshtein distance?

Is there a standard term for the relation on sequences where two sequences are related iff they have a finite Levenshtein distance, or for the equivalence classes it induces?
13
votes
4answers
31k views

What is meant by “evenly divisible”?

"What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" Is it different from divisible?
0
votes
1answer
102 views

2D transformation without rotation

Is there a name for 2D transformation with the least squares adjustment having the following parameters: shift_x, shift_y, scale. Transformation does not use any rotation... Thanks for your help.
10
votes
1answer
488 views

Is there a term for an “inverse-closed” subring of a ring?

I would like to know whether there are established terms for A subring $S$ of a ring $R$ such that $S \cap U(R) = U(S)$; in other words, every element of $S$ which is invertible in $R$ is invertible ...
7
votes
2answers
880 views

Meaning of “a mapping factors over another”?

I was wondering what "a mapping factors over another mapping" generally means? Does it have something to do with commutative diagram in category theory? I have seen this usage in different ...
1
vote
2answers
611 views

Strictly convex at

Another terminology question: If a function $f(x)$ is strictly convex at $y$, does this mean, for an already convex function: a) $f'(y) = 0$, or equally, $y = \arg \min_y f(y)$ b) ...
4
votes
1answer
172 views

Semi-partition or pre-partition

For a given space $X$ the partition is usually defined as a collection of sets $E_i$ such that $E_i\cap E_j = \emptyset$ for $j\neq i$ and $X = \bigcup\limits_i E_i$. Does anybody met the name for a ...
2
votes
3answers
301 views

terminology: set of sets

What is the proper name for "a set of sets"? Is it just a "higher-order set" in general or a "secondary set" in particular? A Wikipedia link would be great. I've been unable to find a special term for ...
1
vote
1answer
1k views

How to describe an algorithm with mathematical notation?

I often have to create new computer science algorithm. The problem come when I have to describe them in a scientific way. I don't know where I should look for to learn how to describe my algorithms ...
11
votes
2answers
415 views

What's the “geometry” in “geometric multiplicity”?

The geometric multiplicity of an eigenvalue is defined as the dimension of the associated eigenspace, i.e. number of linearly independent eigenvectors with that eigenvalue. Here are my questions: ...
2
votes
2answers
736 views

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it? Thanks.
7
votes
2answers
540 views

(k+1)th, (k+1)st, k-th+1, or k+1?

(Inspired by a question already at english.SE) This is more of a terminological question than a purely mathematical one, but can possibly be justified mathematically or simply by just what common ...
5
votes
4answers
258 views

Mathematical notation/name for the number of times a number can be divided by 2

I am using this simple snippet of code, variants of which I have seen in many places: for(int k = 0 ; n % 2 == 0 ; k++) n = n / 2; This code repeatedly ...
34
votes
4answers
4k views

What do Algebra and Calculus mean?

I sometimes see phrases like 'the relational algebra' or 'the lambda calculus'. What is the difference between an algebra and a calculus?
4
votes
3answers
146 views

What's the term for the number of outputs a function has?

That is, if a function's arity is the number of inputs it has, its __ is the number of outputs it has. (Fill in the blank.)
3
votes
1answer
94 views

Asymptotics where the absolute error goes to 0 - what are these called?

Say I have a function $f$ for which $\lim_{x\rightarrow\infty}f(x)=\infty$ and which I'd like to approximate by a simpler function $g$. We say $g$ is an asymptotic for $f$ iff $$ ...
2
votes
1answer
307 views

Does anyone know the name of this curve?

I have come upon the curve with the following parametric equations: $$x(t)=\log(2+2\cos(t))/2$$ $$y(t)=t/2$$ for $-\pi<t<\pi$. It gives the image in the complex plane under $\log(1+z)$ of the ...
7
votes
3answers
402 views

Does this class of cipher have a name? What weaknesses does it have?

Some Background In October I have been asked by the school I teach at to organise and lead 'a hands-on cryptography session' for a bright group of 13 year olds to follow a talk on Enigma by an ...
14
votes
5answers
2k views

What does “formal” mean?

I know the definition of formal power series, power series and polynomials. But what does the adjective "formal" mean? In google English dictionary, does it mean "9. Of or relating to linguistic or ...
9
votes
2answers
2k views

Precise definition of “weaker” and “stronger”?

If I say that $A$ is stronger than $B$, do I mean that $A \Rightarrow B$, or that $B \Rightarrow A$? (Or something else?) I feel like I have seen both usages in literature, which is confusing. ...
1
vote
4answers
9k views

Is sqrt(x) a function? Does it matter if a domain is given? [duplicate]

Possible Duplicates: Reason why the even root of a number always positive Square roots — positive and negative I saw the following during a practice exam: $f(x) = \sqrt x $ for ...
3
votes
3answers
381 views

medians and medoids are to 2, as X and Y are to 3

What is the word for the values derived from an ordered set such that the values divide (by virtue of their positions; not by their value) the set into 3 subsets that have an equal or nearly equal ...
10
votes
4answers
2k views

What is the name of the vertical bar in $(x^2+1)\vert_{x = 4}$ or $\left.\left(\frac{x^3}{3}+x+c\right) \right\vert_0^4$?

I've always wanted to know what the name of the vertical bar in these examples was: $f(x)=(x^2+1)\vert_{x = 4}$ (I know this means evaluate $x$ at $4$) $\int_0^4 (x^2+1) \,dx = ...
1
vote
1answer
209 views

Notation for relations between sets

Are there any customary notation for: $(X\times Y) \cap f \ne \emptyset$ ($f$ is a binary relation, $X$ and $Y$ are sets)? For example $\{ f(x) | x\in X \}$ is commonly denoted as $f[X]$. But are ...
1
vote
2answers
190 views

Is it acceptable to use the term “Algebra of the Real Numbers”

The context is lecture notes on Algebra 2 (that is, elementary algebra and not abstract algebra) for a high school student I'm tutoring. Specifically I'm using the term to refer to the field structure ...
4
votes
2answers
2k views

What does the “closed over”/“closed under” terminology mean exactly and where did it come from?

I've been trying to teach my partner some set theory, and I got thrown for a loop while trying to give her a precise definition of some basic terminology. So we've heard of a set being described as ...
1
vote
1answer
123 views

Not a functor not prefunctor

Are there any special term for the following? A function from the set of morphisms of a category to the set of morphisms of an other category preserving source and destination of every morphism. I ...
1
vote
1answer
217 views

Term for a fully connected balanced graph (Rock paper scissor)

Is there a mathematical, graph theory, game theory term for a graph that is fully connected and balanced evenly with each other node. I'm thinking in situations like Rock paper scissors where each ...
1
vote
1answer
209 views

What is meant by “direct summand in a tensor product”?

I am currently working on the topic of Lie - Algebras and I have stumbled a few times over the expression "direct summand in a tensor product". The text says that $\ V(\lambda) $ as an ...
3
votes
1answer
151 views

What to call the initial members of an ordered set?

If I have an ordered set X = {a, b, c} and another ordered set Y = {a, b}, I know that that ...
11
votes
2answers
726 views

What's the difference between “duality” and “symmetry” in mathematics?

Motivated by the answer to this question--"What kind of “symmetry” is the symmetric group about?", I read the article about dual graph. It is said in this article that "the term 'dual' is used because ...
4
votes
5answers
615 views

How can I succinctly but correctly say that a set is finite?

If I want to say that a set $A$ is numerable but infinite, I can do so like this: $$|A| = \aleph_0$$ What should I use instead to say that a set is finite? $|A|\in\mathbb{N}$? $|A|< \infty$? ...
1
vote
1answer
111 views

Probability: Terminology Question for Convergence in Distribution

I'm currently probability from two different sources: the classic text by Billingsley and the course notes of an instructor at my university. I've run into a terminology conflict that I was hoping ...
8
votes
1answer
539 views

Summation formula name

What is the name of the following summation formula? $$\sum_{k = 1}^n f(k)) = \int_1^{n + 1} f - \frac{f(n + 1) + f(0)}2 + \int_1^{n + 1} f'w,$$ where $w$ is the “sawtooth” function, defined by ...
5
votes
1answer
137 views

Is there a term for a morphism which is surjective on generalized points?

Let $C$ be a category. Recall that a morphism $f : a \to b$ in $C$ is said to be a monomorphism if, for any morphisms $g_1, g_2 : c \to a$, it is true that $f g_1 = f g_2$ implies $g_1 = g_2$. ...
5
votes
1answer
935 views

Difference between formulas and sentences in formal language?

I know that formulas contains free variables and sentences only contains bounded variables. Am I right to say that sentences are equivalent to the properties that structures may have or have not. As ...
9
votes
4answers
671 views

Difference between a “theory” in logic and a “system of axioms”

In logic, a $\Sigma$-theory $T$ is just a set of sentences obtained from the signature $\Sigma$. As I understand, what logician calls "theory" is what a mathematician calls "system of axioms". But ...
6
votes
2answers
322 views

Is there such a thing as the “edge-face dual” of a polyhedron, and is the “edge-face dual” of a cube a rhombic dodecahedron?

The dual of a polyhedron is a polyhedron where the vertices of one correspond to the faces of the other, and vice versa. Is there always a similar correspondence between a pair of polyhedra where the ...
4
votes
3answers
1k views

What is “entire finite complex plane"?

The question is from the following problem: If $f(z)$ is an analytic function that maps the entire finite complex plane into the real axis, then the imaginary axis must be mapped onto A. the ...
56
votes
12answers
6k views

I need mathematical proof that the distance from zero to 1 is the equal to the distance from 1 to 2 [closed]

I didn't know how to phrase the question properly so I am going to explain how this came about. I know Math is a very rigorous subject and there are proofs for everything we know and use. In fact, I ...
6
votes
5answers
980 views

How common is the use of the term “primitive” to mean “antiderivative”?

I don't know if this should actually be asked on the English stackexchange. It seemed like I would find better answers here. I have all but finished an undergraduate degree in mathematics in the ...
10
votes
3answers
977 views

Where is the name “coset” in group theory from?

One of the most important application of "coset", I think, is to prove the Lagrange's theorem, which was not originally stated in the group theoretic terms. In some textbooks I have read about ...
10
votes
2answers
519 views

Origin of the name 'test functions'

This is a very simple question really: where did the name 'test functions', used nowadays when speaking of infinitely differentiable and compactly supported functions, come from? More to the point: is ...
4
votes
1answer
543 views

Involuted vs Idempotent

What is the difference between an "involuted" and an "idempotent" matrix? I believe that they both have to do with inverse, perhaps "self inverse" matrices. Or do they happen to refer to the same ...