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

learn more… | top users | synonyms (2)

1
vote
1answer
105 views

Sufficient/necessary vs. weaker stronger

I know what sufficient resp. necessary means, but I'm confused, when our professor uses the terminology weaker resp. stronger. I couldn't yet find out, what the translation of these pair of words to ...
1
vote
2answers
65 views

Is there a particular notation for a function confined in a set?

For example $f:\mathbb{R}\to\mathbb{R}$ is a function. How to simply express a correspondent function $g:\mathbb{Q}\to\mathbb{R}$ such that $g(x)=f(x)$, $\forall x\in\mathbb{Q}$?
1
vote
1answer
113 views

Foam-like graphs

What's the "official" name of a connected planar graph consisting entirely of polygons (cycles), glued together at edges, e.g. - among other things - without "end vertices" (of degree 1) and without ...
1
vote
1answer
70 views

Notation and naming for two operations with $p$-form valued $n$-forms

While trying to answer my other question I found I never heard about vector-valued differential forms. I've been searching for them in various mathematical physics books, but didn't get too much. I'm ...
1
vote
1answer
731 views

What is the meaning of evaluating the divergence at a _point_?

Reading this first, Divergence (div) is “flux density”—the amount of flux entering or leaving a point. Think of it as the rate of flux expansion (positive divergence) or flux contraction (negative ...
1
vote
1answer
243 views

Is there a different name for strongly Darboux functions?

A function $f\colon\mathbb R\to\mathbb R$ is called Darboux function, function with Darboux property or function with intermediate value property for for any $a<b$ and any $z$ between $f(a)$ and ...
1
vote
1answer
166 views

What is an honest basis?

In a comment to this question, the commentator stated that "the monomials form an honest basis for your vector space". To be honest, I never heard of that. Is this something elementary?
1
vote
1answer
227 views

What does Linear Congruential mean?

How does one interpret the terms "Linear" and "Congruential" as in a "Linear congruential RNG"? I am used to linearity by $f(ax)=af(x)$. This does not seem to me to hold true in this case ($\bmod$). ...
1
vote
2answers
786 views

What does a condition being sufficient as well as necessary indicates?

I have a question in a book I am solving(Discrete Structures by Kolman, Busby & Ross). I am unable to make sense from the question. It is stated below, Show that k is odd is a necessary and ...
1
vote
3answers
222 views

How to define $-\infty$?

I think I understand the fundamental concept of infinity. Elementary mathematics define $\infty := \frac{x}{0}$, for every $x$. And also $\infty := \frac{-x}{0}$ for every $x$. I know only one ...
1
vote
1answer
115 views

Is there a special name for a semigroup whose multiplication is a constant function?

Let $S$ be a (commutative) semigroup with distinguished element 0 such that $ab=0$ for $a,b\in S.$ Of course this is a very simple family of semigroups, defined only by their cardinality. Does it ...
1
vote
3answers
150 views

Matrix with exactly one 1 in each row

Is there a name associated to rectangular matrices $M \times N$ that have exactly one entry equal to $1$ in each row and $0$ everywhere else?
1
vote
2answers
143 views

What is the name for a function of a matrix that changes the matrix size?

I have a set of functions that map square matrices with $n$ rows and columns to square matrices with $k < n$ rows and columns. Is there a name for this property? I know that 'projection' would be ...
0
votes
1answer
23 views

Need help in understanding $ord_p{a}$ as used in Theorem 1.1 from “On Some Exponential Equations Of S. S. Pillai”

I have a question about very early argument in the proof of Thereom 1.1. Theorem 1.1 of On Some Exponential Equations of S.S. Pillai states that if $a,b,c$ are nonzero integers with $a,b \ge 2$, then ...
0
votes
1answer
36 views

Notation for permutation corresponding to the action of a group element

Let $G \times X \to X,\ \ (g,x) \mapsto g.x$ be an action of $G$ on $X$, i.e., $e.x = x$ for all $x \in X$; $gh.x = g.(h.x)$ for all $g \in G$, $x \in X$. For a fixed $g \in G$, how should I refer ...
0
votes
2answers
144 views

Is an unit-cube polyhedron? What about other platonic solids?

Definitions According to my linear programming course and screenshot here (Finnish), a polyhedron is such that it can be constrained by a finite amount of inequalities such that $$P=\{\bar x\in ...
0
votes
1answer
71 views

What does $f$ is measurable as a function $f^{-1}(\mathbb{R})\to\mathbb{R}$ mean?

I saw a question where we have $\overline{\mathbb{R}}:=\mathbb{R}\cup\{\pm\infty\}$ and $(X,S)$ is a measurable space, $f:\, X\to\overline{\mathbb{R}}$ In one part I was told to assume that $f$ is ...
0
votes
1answer
120 views

Correct reading of Set builder Notation?

could anyone please let me know the correct reading(sentence form) of set builder notation, confused with different interpretation in different resources. Many Thanks
0
votes
1answer
436 views

Elements of order $n$ in a cyclic group of order $N$

The number of elements of order $n$ in a finite cyclic group of order $N$ is $0$ unless $n|N$, in which case it is $N/n$. Is "the number of elements of order $n$" referring to the number of ...
0
votes
1answer
75 views

What is the meaning of “countable spread”?

I encountered an example that said: A Tychonoff 2-starcompact space of countable spread which is not $1\frac{1}{2}$-starcompact. My question is this: What's the meaning of "countable spread" ?
0
votes
1answer
90 views

Whether to use 'OR' or 'AND'

My doubt is: while solving equations or inequalities consisting of absolute values when should we use the conjunction 'OR' and when to use 'AND'? whats the difference between them ?
0
votes
1answer
927 views

A Set is a collection of well defined and distinct objects. What is a collection of well defined objects without being distinct called?

A set is a collection of well defined and distinct objects, considered as an object in its own right. What is the mathematical term for a collection of well-defined objects without distinction ...
-8
votes
3answers
714 views

Why direction makes difference between scalars and vectors?

I always hear that there are scalar fields and they are different from vector fields in that vectors have a direction whereas temperature has not. For instance, here is a professor saying that, ...