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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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 ...
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 ...
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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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 ...
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 ...
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 ...
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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 ...
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 \...
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 ...
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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 ...
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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 ...
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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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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 $K$, ...
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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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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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 ...
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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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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.
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?
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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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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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 ...
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-...
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?
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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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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....
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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 ...
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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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 ...
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 ...
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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 ...
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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 ...
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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 ...
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 ...
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 ...
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 ...
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: ...
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 ...