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

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0answers
24 views

Are constants a special case of coefficients?

What I hope to understand better, is the relation between constants and coefficients. Consider the following polynomial: $$3x^2+2x+5$$ What are the coefficients in the expression? Obviously, 3 and 2 ...
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0answers
12 views

What do you call the projected curve of a circle/ellipse on a cylinder?

What do you call the projected curve of a circle/ellipse on a cylinder? (The figure shows a circle projected on a cylindrical surface) See Figure (Circle Projected on a Cylinder) EDIT: If a name ...
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0answers
21 views

permutohedron vs permutahedron

Why are there two spellings for the terms denoting the sets $$\mathrm{Conv}\left(\left\{(\sigma(1),\ldots,\sigma(n))\,\middle|\, \sigma\in S_n\right\}\right)\qquad(n\in\mathbb{N}^+)\,,$$ namely, ...
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0answers
15 views

Term for listing all possble integers that add up to a specific total

Pretty simple question, much like we use 'factorise' to describe finding the factors of a number, is there a term for finding all the (integer) numbers that can be added up in any combination to the ...
3
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1answer
70 views

The maximal rotation matrix

Let's consider two numbers calculated for a rotation matrix which are: $s_e=$ the sum of all entries of a matrix $s_a=$ the sum of absolute values of all entries for a given matrix. It ...
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0answers
18 views

If a Galois connection does exists, how is it called?

Let $\phi$ be a function from a poset $B$ to a poset $A$. $f \mapsto \min \{ g\in B \mid \phi(g) \geq f \}$ is called the lower adjoint of $\phi$ and $\phi$ is called an upper adjoint. These two ...
3
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1answer
114 views

Why is ring of integers $\mathcal O_K$ called ring of integers - what properties of $\mathbb{Z}$ does it inherit?

I was wondering why ring of integers $\mathcal O_K$ for field $K$ is called ring of integers. Definition says that elements in this ring will be a solution for monic equation with coefficients of ...
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3answers
727 views

Is a data set really a set?

Originally I thought that in statistics, a data set is just a set of real numbers, and that was it. But in the case of a set, there can only be one instance of any given entry, e.g. in set theory $$\...
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1answer
384 views

Graph nomenclature

This concerns graphs that are sets of vertices and edges G={V,E}, not graphical depiction of functions. Imagine a graph that is a 2D square mesh of vertices. Such a graph can be constructed, for ...
3
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2answers
104 views

What are “words”?

Related but not duplicate. I am reading Classical Mathematical Logic by Richard L. Epstein, page $3$: B. Types When we reason together, we assume that words will continue to be used in the ...
2
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0answers
35 views

Names for related pairs of angles

I seek the names (if they exist) of two relationships between angles. Two angles are complements of each other if they add up to a quarter circle. $\sin\alpha=\cos\beta$ and vice versa. Two angles ...
2
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0answers
64 views

Unclear passages in the paper “On a New Class of Theorems in Elimination Between Quadratic Functions” by J. J. Sylvester

I'm writing an essay about the origin of some mathematical terms in the work of J. J. Sylvester. He first used the word matrix in his paper Aditions to the Articles "On a New Class of Theorems" and "...
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1answer
13 views

Nichtnegativstellensatz the same as Handelman's Theorem?

Wikipedia on "Handelman's theorem: If $K$ is a compact polytope in Euclidean $d$-space, defined by linear inequalities $g_i ≥ 0$, and if $f$ is a polynomial in $d$ variables that is positive on $K$, ...
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10answers
15k 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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0answers
21 views

Is the phrase “random number function” contradictory? [on hold]

If a Function is something that produces an output from an input(s) and is consistent, then the phrase "Random Number Function" should not be allowed, right?
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0answers
18 views

Name for a directed set that is also a partial order but not necessarily a semilattice?

Is there a term for a structure $(S,\preceq,+)$ where $+$ is commutative, idempotent, and monotone with respect to $\preceq$? That is, for all elements $s$ and $t$, $s+t=t+s$, $s+s=s$, and $s\...
2
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2answers
113 views

How do you pronounce Richard Courant's surname?

Since his surname looks rather French than German, I started wondering how you pronounce his name. In particular, I'd be interested in how he would have pronounced his name himself (since I already ...
0
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1answer
13 views

Is reverse lexicographic order the same as graded reverse lexicographic order?

I want to make sure whether the two monomial orderings are actually the same thing. I am confused because the Cox book on Ideals, Varieties and Algorithms mentions only the graded reverse ...
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2answers
49 views

What's the difference between substitution and equality?

Is $2$ a substitution for $1+1$, or equal to $1+1$? In this case both seems true, but I was wondering if there really is a difference. Whenever there is an equality $A=B$, is it also true that $B$ is ...
0
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1answer
17 views

How to read partial ordering in a set?

Let $X$ be a partially ordered set with partial order $\preceq$. Then how can we read $x\preceq y$. Is it $x$ less than or equal l to $y$.?
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4answers
8k views

What is the difference between an axiom and a postulate?

I hear about axioms in set theory and postulates in geometry, but they seem like the same thing. Do they mean the same thing but then are used in different instances or what? Is one word more ...
2
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2answers
42 views

A question about the term “depressed cubic”

The depressed cubic equation is a cubic equation of the form $x^3+px+q=0$. This expression sounds strange especially for someone that English is not his mother tongue. Why this equation is called "...
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2answers
38 views

Useful analogy to interpret the notion of evolutionary stable strategy (ESS)

I am seeking a good analogy to understand the concept of evolutionary stable strategy (state) Let $\pi$ denote the fitness of a population, $\pi_{ij}$ is the fitness of strategy $i$ against strategy $...
1
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1answer
48 views

Vector fields (on a manifold) and terminology

I read in several books (Do Carmo, Riemannian Geometry or John M. Lee, Smooth manifolds) that a vector field $X$ on a smooth manifold $M$ is a mapping which associates to each point $p \in M$ a ...
2
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0answers
16 views

What does it mean to say a point is uniquely mapped?

I am looking at space filling curves. Essentially their is a mapping $f: I \to \mathcal{Q}$ where I is an interval in $\mathbb{R}$ such as $[0,1]$ and $\mathcal{Q}$ is a square $[0,1]^2$. For the ...
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2answers
97 views

What do mathematicians mean when they say “form”?

As in differential form, modular form, quadratic form? I'm sorry if this is a really silly question.
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1answer
32 views

All directed paths between any two vertices have the same length

Is there a term for the condition that, given some directed graph $G = (V, E)$, for all $v, w \in V$ every directed path from $v$ to $w$ has the same length as every other?
2
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1answer
43 views

Are there more proper terms for “between, inclusive” and “between, exclusive”?

I searched for this, but all I found was an English usage result. However, I am strictly asking about ranges of numbers, not "normal" English. So, are there a terse terms for: inclusive between, ...
0
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1answer
42 views

Specifying from the general in probability: Does it work? [closed]

If the average classroom AC holds 30 students, and 1 in 10 students throughout the US has a probability of having condition A, does that mean there's a 300% chance there's a student in classroom AC ...
2
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4answers
134 views

What is a constant?

The word "constant" is used in such expressions as "The derivative of a constant is $0$." What does it mean? (I will post my own answer here, but I'm sure lots of others can have fun with their own ...
0
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0answers
22 views

Names for the vector spaces $T(V)$ and $S (V)$

Are there any names for the vector spaces $T(V) = \bigoplus_{n\geq 0} V^{\otimes n}$ and $S(V)= \bigoplus_{n\geq 0} V^{\otimes n}/\Sigma_n$? The best thing I could come up with is "the underlying ...
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2answers
33 views

Difference between Ordering and Order?

I am confused by the two terms order and ordering. I am learning on Ideals, Varieties and Algorithms by Cox et all. The context is monomial orderings and Gröbner basis on polynomial rings. How are ...
26
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7answers
3k views

Is there such a thing as a matrix of functions?

Do we ever put functions as entries of a matrix? If so, are these matrices used in linear algebra or do they have some other special use? There have been minor not neccessarily conflicts per se, but ...
2
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1answer
55 views

What does it mean in general to show something is well defined? [duplicate]

There is another post that addresses this but quickly fix the problem to be something in arthmetics, and in turn what it means for that arithematics problem to be well defined. I have never ...
3
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0answers
34 views

What does “Borel space”, unqualified, refer to?

For examples of use, Google "in Borel space", without the quotes. I'm thinking it means either ℝ equipped with its Borel σ-algebra, or to Borel spaces in general (that is, topological spaces with a σ-...
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1answer
27 views

difference between variance and covariance

What exactly is the physical interpretation of variance (in terms of a data set) and the difference between variance and co-variance matrices?
2
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1answer
40 views

Alternative Definition of Contravariant Functor

Given two categories, $C$ and $D$, a covariant functor is usually defined as a regular functor $C \to D$, whereas a contravariant functor is usually defined as a regular functor $C^{op} \to D$. ...
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1answer
30 views

What does “coefficients from all of $\mathbf{F} _q$” mean

I was reading Wikipedia's page on Ring Learning with Errors, and came to wonder what is meant by "with coefficients from all of $\mathbf{F} _q$" which is a requirement for the set of known polynomials....
2
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1answer
70 views

What is $x \mapsto f(x)$ called?

A function is defined by either A function $f: A\to B$ is defined by $\color{green}{x\mapsto f(x)}$ or $ \begin{align}f:\quad&A\to B\\&\color{green}{x\mapsto f(x)}\end{align}$ Is ...
0
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0answers
27 views

A question of terminology regarding exceptional curve or is it divisor.

So I kept on reading the book by Griffiths and Harris called Principles of Algebraic Geometry and I've seen a definition of exceptional divisor of the first kind. On page 487: A smooth rational ...
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0answers
10 views

Relationship Between Variables Both Growing/Decreasing, not Proportional

So proportional is when the variables are equal to one another when multiplied by a constant. What is the term for something like weak proportionality that when one variable increases the other will ...
1
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1answer
43 views

Is “closedness” a proper word?

In one of my papers I had to prove a list of properties of a set, say, $S=\{a,b,c\}$. Among them we have a fact that $S$ is downward closed with respect to a binary relation $R$. I found it awkward to ...
42
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12answers
5k views

Does “Doing a thing to both sides of an equation” have a name?

A two part question. 1 True or False: when working with an equation or inequality, everything that you do is either: a substitution, or an operation performed on each side Note that algebraic or ...
1
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1answer
47 views

Ring->module->$R$-algebra, Field->Vectorspace->algebra

I haven't done any mathematics for a long time, and I have forgotten some things. I want to try to remember some of the words and how they interact. A module is a 'vectorspace over a ring' rather ...
0
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0answers
18 views

Is Site Percolation with Bernoulli variables i.i.d. independent and identically distributed?

I cannot understand the identically distributed part in the i.i.d assumption. Consider a site percolation where each event is a Bernoulli variable. Does this mean ...
0
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2answers
43 views

How to call the region bounded by a hyperbola

Given an hyperbola, is there a mathematical name that describes the region/area bounded by one arm of the hyperbola? In this image the area is marked grey. To clarify my question: I'm looking for a ...
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1answer
28 views

What is the definition for totally ramified extension for a global field?

What is the definition for totally ramified extension for a global field? For local fields it means the maximal prime ideal generated from the uniformizer totally ramifies. But what is the definition ...
2
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1answer
70 views

Is there an equivalent word for '3/4?'

It's already known that the most of the quarter fractions have a single word equivalent that correspond with its numerical counterpart, such as '1/4' is a quarter, '1/2' is half, and '4/4' is the same ...
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0answers
23 views

Binary tree traversal with fixed final node

What type of traversal is this called? Given a root node A and final node B: ...
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2answers
4k views

Names of higher-order derivatives

Specific derivatives have specific names. First order is often called tangency/velocity, second order is curvature/acceleration. I've also come across words like Jerk, Yank, Jounce, Jolt, Surge and ...