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

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7 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 ...
1
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0answers
16 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 ...
8
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3answers
718 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 $$\...
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 ...
3
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2answers
102 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 ...
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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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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\...
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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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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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2answers
48 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 ...
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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
47 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
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
96 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?
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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 ...
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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 $...
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, ...
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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 ...
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 $C^{op} \to D$. ...
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 ...
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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 ...
0
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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....
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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 ...
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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 ...
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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
votes
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: ...
4
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1answer
46 views

Are Free Groups the “Smallest Group” Containing their Generators

I apologize if this is a duplicate; I was not sure how to search for this. When I say "the smallest group" I mean unique up to isomorphism of course. Specifically, is "the smallest group containing ...
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4answers
515 views

Proving a theorem, what is meant by sufficiency and necessity?

I am looking at the proof of a theorem and the proof begins by saying ...is the proof of the sufficiency part of this theorem so we just need to establish the necessity of the condition. What ...
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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 ...
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0answers
7 views

How is the threshold probability $p_c$ defined for oriented site percolation?

The threshold probability for unoriented site percolation is such that \begin{eqnarray*} \mathbb{P}_{p} & = & \underset{v\in\mathbb{\mathbb{L}}^{d}}{\prod}\mu_{v}\\ \theta(p) & = & \...
6
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5answers
249 views

List of theorems named after non-human animals [closed]

I think it would be entertaining if we could come up with a list of theorems named after non-human animals (so excluding names like "Gauss's lemma" and the like). So far, I have only encountered two, ...
3
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0answers
51 views

Are the elements of a module also called vectors?

Are the elements of a module also called vectors? Or if someone says 'vector', are they talking only about a vector space? If no context is given, are there some standard assumptions?
2
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1answer
42 views

Does absorbing Markov chain have steady state distributions?

If I am not mistaken, the steady state distribution is independent of initial state distribution, and regular Markov chains satisfies this definition. On the other hand, since the row of each ...
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1answer
27 views

Site Percolation and S-clusters with $n\times m$ grid where $n\not =m$?

Consider a site percolation but change the dimension of the lattice from $n\times n$ to $n\times m$ where $n\not = m.$ S-clusters are defined for $n\times n$ lattice. The occupation of each site are ...
2
votes
2answers
64 views

Is there a word for saying that $\Pr(A \mid B) = \Pr(B \mid A) = 1$?

If I have two events $A$ and $B$, I can express the fact that $\Pr(A \cap B) = \Pr(A) \cdot \Pr(B)$ by saying that $A$ and $B$ are independent. What word can I use to say that $\Pr(A \mid B) = \Pr(B \...
2
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2answers
54 views

Notation for the set of zero divisors in a ring

If $R$ is a nonzero ring with identity then I have seen the group of units denoted by $R^{\times}$ or possibly $R^*$ in some texts. In a classical ring there is a trichotomy which declares each ...
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0answers
21 views

Terminology for a process with subcritical, critical, and supercritical cases?

I've noticed that, in a number of domains in pure and applied mathematics, there are processes or structures involving exponential growth or decay where the process splits into three cases: a ...
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1answer
17 views

Sites always closed in Bond percolation?

The page 2 of Percolation by Bollobas et all (2009) contains this picture where the left is for the site percolation and the right for the bond percolation. The filled circles on the left are open ...
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0answers
15 views

Absorbing State vs Closed Communicating Class

According to Wikipedia, A set of states C is a communicating class if every pair of states in C communicates with each other. A communicating class is closed if the probability of leaving the class is ...
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0answers
31 views

Name for quiver representation

Let $Q = (Q_0, Q_1)$ be a quiver, and pick some $i \in Q_0$. Define the quiver representation $M$ by $$M_j = \begin{cases} k & \text{ if there is a path from $i$ to $j$,} \\ 0 & \text{ ...