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

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4answers
53 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
22 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 ...
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2answers
44 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
34 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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1answer
18 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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0answers
51 views

Mathematicians with hyphenated names [on hold]

I just found out that the Levi-Civita symbol is named after only a single person. Which other mathematical theorems or objects are named after mathematicians with hyphens in their names?
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0answers
9 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 ...
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5answers
5k views

What's the difference between stochastic and random?

What's the difference between stochastic and random? I've read in the portuguese wikipedia that there's a difference, but I still didn't see this point on english wikipedia.
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19answers
6k views

What is the difference between a point and a vector

I understand that a vector has direction and magnitude whereas a point doesn't. However, the course note that I am using states that a point is the same as a vector. Also, can you do cross product ...
3
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1answer
293 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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2answers
274 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 $\tau$?
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4answers
55 views

Is there a name for 1-x or x-1?

I've read the wikipedia entry on the multiplicative inverse: http://en.wikipedia.org/wiki/Multiplicative_inverse Where it clearly says that $x^{-1}$ is the inverse. But I feel like x-1 or 1-x has a ...
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1answer
22 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
28 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
7 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 ...
0
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2answers
21 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
24 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.
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4answers
278 views

What is linearity?

Once someone asked me the question "What is linearity?" in a proficiency exam. I went hot and cold all over. Although, I heard and even used the term linearity many many times, I had not really ...
0
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1answer
26 views

Need help to understand some terminology in discrete math

1) "Suppose that f is a function from set A to itself." 2) "(...)from the set of real numbers to itself." In these two sentences, what does "to itself" mean? Is this the same as saying that 1) is f: ...
2
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1answer
38 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 ...
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0answers
22 views

“two sets differ” in vs by “exactly 1 element”, in both cases is symmetric implied?

When a mathematician says, "two sets differ in exactly 1 element", what precisely do they mean? Does, "two sets differ by exactly 1 element", mean something different? Given $ A = \{1,2,3\}, B = ...
0
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0answers
35 views

What's the right way to write big-O?

I always write $\mathcal{O}(n)$ (\mathcal{O}(n)). But I frequently see $O(n)$ (O(n)), probably because it's shorter and more ...
2
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2answers
990 views

name for a rational number between zero and one?

I'm searching for a unified name to convey for the concept that a number will always be between zero and one. Some info for context: in probability we've got a number between 0 and 1. Percentages ...
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2answers
2k views

What is the difference between an axiom and a postulate?

I here about axioms is set theory and postulates in geometry, but they seem like the same thing. Do the mean the same thing but then are used in different instances or what? Is one word more ...
0
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0answers
32 views

Terms for particular equivalence relation and partition?

Let $T$ be a set of sets. Let $\equiv$ be an equivalence relation on $\bigcup T$ defined by the formula $$a\equiv b \Leftrightarrow \forall X\in T:(a\in X\Leftrightarrow b\in X).$$ Let $S$ be a ...
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0answers
11 views

Term for “interval with a step size”

I'm looking for a term for "interval with a step size". Let's write such an "interval" as an interval-like tuple $I=[from, step, to]$. Then $I$ is defined as $I=\{x|x=from+n \cdot step, n \in ...
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1answer
40 views

How to call a shape (2D or 3D) that has no dents in it?

Is there a name for a shape that has no dents in it? The shape can exist in 2D or 3D space. It is best demonstrated with a picture: On the left is a shape that has no dents in it, and on the right ...
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1answer
41 views

What's the terminology for whether a number is positive or negative?

Is there a word for the quality of a number to be either positive or negative? Consider this question: What's the ... (sign/positivity/negativity, but a word that could describe either) of number x? ...
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2answers
51 views

Terminology for $1/(e^x+1)$?

$ \frac{1}{e^x+1} $ and $ \frac{e^x}{e^x+1} $ Just wonder if either of the above function has a term/name associated with it? Or they are just functions that look beautiful without names? Maybe they ...
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0answers
11 views

Is “nonanticipating” a measurability property of a function or something more?

I have been reading some operations research papers that throw in the term "nonanticipating" at key points in the exposition, but I can't figure out precisely what they mean. My best guess is that ...
3
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0answers
44 views
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6answers
699 views

Dictionaries and resources for translation of mathematical terminology

Nowadays English seems to be the most frequently used language in mathematics. (Although plenty of papers and books are published in other languages, e.g., Russian, French, German and Chinese.) ...
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0answers
104 views

Have these (extremely simple) classes of algebraic structures been considered in the literature? If so, what are they called?

Questions. Have the following kinds algebraic structures been considered in the abstract algebra literature etc.? If so, what are they really called? (I have used made-up terminology for the sake ...
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2answers
58 views

$\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ notation

Define $\mathcal N$ $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ Does $\mathcal N$ has a special name and standard notation?
2
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1answer
40 views

Is this an ordinary differential equation?

If a differential equation contains only ordinary derivatives of one or more functions with respect to a single independent variable it is said to be an ordinary differential equation (ODE). If ...
0
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1answer
18 views

Is this ODE linear?

Determine whether the given first order differential equation is linear in the following variables: $(y^2-1)dx+xdy=0$; in x and y I'm pretty confused here. I've seen $\frac{dy}{dx}$ but what do $dy$ ...
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0answers
24 views

For every pair of vertexes there is at most one path

A directed graph such that for every pair $(A;B)$ of vertexes there is at most one path from $A$ to $B$, is there are name for this concept? @Ishfaaq: Your answer is wrong, see such a digraph which ...
2
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1answer
29 views

Is there a name for spaces that always have local sections?

Given a continuous map $p:E \rightarrow B$ Suppose for every point $b \in B$ and a point $x \in p^{-1}b$ in the fibre of it, there is an open set $V$ of $B$ that contains the point $b$ such that ...
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0answers
34 views

In linear algebra, what is the word used to state that two linear equations are the same line?

If we have to solve a system of linear equations with two linear equations. What is it called if both of these two lines are the same? I.e. the first line is $x+y=1$ and the second line is ...
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1answer
13 views

Signal “representation” terminology

A paper I'm reading now defines invariant signal "representations" as those functions $\Phi$ of signals $x$ in a Hilbert space such that $\Phi(g\cdot x) = \Phi(x)$ where $g\cdot x$ is the action of ...
0
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1answer
26 views

The proper term to describe a category of geometric shapes.

I'm looking for geometric terminology that would describe this kind of shape, if there is a term for it. Picture any arbitrary closed 2D shape. Picture the smallest circle that will completely contain ...
1
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1answer
37 views

Definition Fixed Element

I am looking for the definition of a "fixed element". The context is "Let G be a group and let a be one fixed element of $G$. Show that $H_a = \{x \in G | xa=ax \}$ is a subgroup of $G$." Thanks.
1
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0answers
22 views

operator vs operation vs function vs procedure vs algorithm

I have a vague understanding of what operator, operation, function, procedure, algorithm mean in general. I am heavily biased towards computer science. Do you agree with them? What are the generally ...
1
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0answers
30 views

Eigenvalues that are functions

Let us have the Laplacian on a compact manifold $M$. Suppose I have some equation of the form $$-\Delta u(x) = f(x)u(x).$$ If $f \equiv c$ were a constant, this would be an eigenvalue problem ...
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0answers
20 views

The space of alternating multilinear forms

I was just wondering if there is a standard (or even just usual) notation for the space of alternating $k$-linear forms on an $F$-vector space. I know that this space is naturally isomorphic to the ...
0
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1answer
16 views

Number of variables and dimension of a function

Why is a function $f(x)$ called a single-variable function if it has coordinates represented by $x$ and $y$? Can it be called a 1D function if its plot is 2D? Subsequently, can two-variable functions ...
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3answers
160 views

Is there a name for a semigroup whose idempotents form a subsemigroup?

For a semigroup $S,$ I will denote by $E(S)$ the set of all idempotents of $S$. For $X\subseteq S,$ let $X^2$ mean $\{xy\,|\,x,y\in X\}.$ Is there a name for the class of semigroups $S$ such that ...
18
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4answers
3k views

Why is an image called an “image”?

Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its ...
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6answers
2k views

Is there a name for the function $\max(x, 0)$?

Is there a name for the function $ \max(x, 0) $? For comparison, the function $ \max(x, -x) $ is known as the absolute value or modulus of x, and has its own notation $ |x| $
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1answer
40 views

Definition of a certain matrix

I remember I came across matrix of the form $$\begin{bmatrix} 1 & 0 & 0 & 0\\ 1 & 1 & 0 & 0\\ 0 & 1 & 1 & 0\\ 0 & 0 & 1 & 1\\ \end{bmatrix}$$ There ...