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

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3
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2answers
207 views

Meaning of “-oid” in mathematical concepts?

Some mathematical concepts are ended with "-oid", such as Matroid, greedoid, groupoid. What does that mean? Do these concepts share something in common? Thanks!
4
votes
2answers
3k views

Slope of a nonlinear curve at a single point

This part of my microeconomics lesson plan has me baffled. Consider for example the nonlinear continuous and differentiable function Y = f(X) = X 2 + 4. Suppose we want to know its slope at the ...
4
votes
0answers
285 views

Torsion-free fundamental group.

Is there a name for spaces whose fundamental group has no torsion? And what, if any, are some nice properties of these spaces?
5
votes
1answer
124 views

A prime poset of ideals

Let $A$ be a ring (commutative unital), and $\mathcal I$ be a nonempty family of proper ideals of $A$. I will say that $\mathcal I$ has property $\dagger$ if for any $\mathfrak a\in\mathcal I$ and ...
2
votes
2answers
609 views

What is the difference between two variables being proportional versus being directly proportional?

I hear these expressions being thrown around, and realize that "proportional" may also incorporate inverse proportion, but are there any other differences?
4
votes
3answers
1k views

Term for a group where every element is its own inverse?

Several groups have the property that every element is its own inverse. For example, the numbers $0$ and $1$ and the XOR operator form a group of this sort, and more generally the set of all ...
1
vote
2answers
202 views

Is the term true? $\frac{\theta}{\theta - 1 } = \frac{1} {\theta-1} + 1$

Why is the following term true? What is the corresponding rule or how is it transformed? $\frac{\theta}{\theta - 1 } = \frac{1} {\theta-1} + 1$ Thanks!!
1
vote
0answers
52 views

Terminology for an operator that inverts itself?

I am familiar with the term involution for a function that inverts itself, and was wondering if there is a similar term for binary operators like XOR. For example, $a \oplus b \oplus b = a$ for any $...
4
votes
1answer
208 views

Where does ergodic come from?

In math you usually understand why terms such as triangle, function, polynomial, category or even vector came to be. However where does the word ergodic come from? Does it have a meaning in another ...
2
votes
2answers
118 views

Exact meaning of “consists of”

What does consists of mean exactly, say in an arithmetic progression of length $n$ consists of prime numbers? Are there only prime numbers or must there be at least one prime number in the progression?...
2
votes
1answer
95 views

What are these coordinates on $\mathbb S^n$ called?

I vaguely remember some special kind of coordinates on the sphere $\mathbb S^n$ as a Riemannian manifold, but I have forgotten their name: They are defined by choosing a great $\mathbb S^{n-1}$ and ...
2
votes
1answer
64 views

Use of the term “normal section” in a theorem of Maria Lucido.

Prop. 3 in this paper (p.135) states Let $G$ be a solvable group with $\text{diam}\Gamma(G)=4$. Then either $l_F(G)\leq 3$ or $l_F(G)=4$ and $G$ has a normal section isomorphic to $H$. ($H$ is ...
0
votes
0answers
83 views

Correct term for the set of numbers which cannot be expressed in a particular base

For every base there's a set of fractions that can't be expressed with the exponent in that base, for instance 1/3 cannot be represented in decimal and 1/10 can't be represented in binary (...
4
votes
0answers
184 views

matrix representation of operator

Vector $\vec v\ $ in basis E = $[\vec e_1 \vec e_2 \ldots \vec e_n]$ $$\vec v = E \ \begin{bmatrix}v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix}$$ Now, operator acts upon it $$A(\vec v) = v_1 A(\vec ...
6
votes
3answers
173 views

What is this property called?

Let $(V,\,+,\,\cdot\,)$ be a vectorspace and $D\subset V$ a set with the following properties For $\;\lambda D:=\{\lambda d\mid d\in D\}\;\textrm{ and}\;\;\lambda,\, \mu\ge0$: $$0\in D$$ $$\bigcup_{\...
0
votes
1answer
73 views

Is there a name for a lattice that is isomorphic to its dual?

If we have a lattice and we invert the order, we again obtain a lattice, called the dual lattice. Is there a name for a lattice that is isomorphic to its dual lattice?
2
votes
1answer
92 views

What do you call this generalization of a module?

A module $M$ is an Abelian group with the extra property that any element $m \in M$ can be multiplied by any element $r$ in a ring $R$. I want to relax this definition so that the $M$ need not be an ...
0
votes
1answer
2k views

Solving/Proving from first principles?

When asked to solve/prove something from first principles, what do they mean by that? They expect you to use only axioms or basic properties or both or it can be a bit more subjective understanding of ...
1
vote
1answer
150 views

Questions on Basic Terminology in Mathematical Logic

As a beginner, I'm overwhelmed by the usage of terminology , such as theory, model, interpretation, structure et al, which are omnipresent in Mathematical logic. Here's my understanding about them: ...
2
votes
2answers
993 views

What are matrix coefficients in linear algebra?

What are matrix coefficients in linear algebra? And what does it mean "integer matrix coefficients"?
2
votes
2answers
3k views

Is the tangent function (like in trig) and tangent lines the same?

So, a 45 degree angle in the unit circle has a tan value of 1. Does that mean the slope of a tangent line from that point is also 1? Or is something different entirely?
3
votes
3answers
201 views

Algebra terminology: stable

What is the meaning of a set being 'stable'? Is this the same as a set being closed under an operation? To provide some context, the reference I saw is to a set $M$ being 'stable' where there is a ...
1
vote
1answer
2k views

Defintion of Upper & Lower Riemann Sum

I recently came across the terms: 'upper Riemann sum' and 'lower riemann sum'. Are they represent the same things as of 'upper sum' and 'lower sum' defined as follows.
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vote
0answers
72 views

Elliptic curve terminology confusion

I've been reading a paper that says "Let $E(K)$ be an elliptic curve..." where $E(K)$ means the $K$-rational points of $E$ (where $K$ is a number field). I've seen phrases like "Let $E/K$ be an ...
15
votes
2answers
3k views

What happens if we remove the requirement that $\langle R, + \rangle$ is abelian from the definition of a ring?

Ever since I learned the definition of a ring, I've wondered why the additive group is required to be abelian. What happens if we allow $\langle R, + \rangle$ to be nonabelian as well as $\langle R, \...
1
vote
1answer
443 views

“Base is degenerate IFF its corresponding basis matrix is singular”: degenerate with solution and degenerate without solution?

Statement "Base is degenerate IFF its corresponding basis matrix is singular" is wrong according to my Linear-programming teacher Mat-2.3140 in Aalto University (translated from Finnish here/here) ...
9
votes
0answers
117 views

Topological Space in which every compact subset is metrizable

Is there an (more or less) established name for the class of topological spaces in which every compact subset is metrizable? This is true for example in (LF)-spaces (inductive limits of Frechet-spaces)...
0
votes
1answer
103 views

Does this object have a category-theoretic name?

I have morphisms: $$ f : A \to B \\ g : B \to C $$ The composition is: $$ g \circ f : A \to C $$ In the function $(g \circ f)$ we call $A$ the domain and $C$ the codomain (or range). I'm ...
0
votes
1answer
20 views

How tuples or rows do usually called in statistics?

Is there a special term for couple of measured values of single event in statistics? This is called record, tuple or ...
1
vote
2answers
45 views

Using “adjunction” to refer to the act of taking adjoints of operators

I have an especially flabby terminology question. How acceptable is it, in your opinion, to use the word "adjunction" to refer to the process of taking adjoints of operators on a Hilbert space? ...
1
vote
2answers
153 views

How is this equation called?

I'm trying to figure out some math problems. In particular I have this "In an office you have 6 clerks. How many ways can you select a team of 3 clerks?" and the solution given is: $$\binom{6}{3} = \...
2
votes
1answer
54 views

Terminology of a space in real-analysis

Since this is a very simple question, i didn't want ask this here not to bother you, so i saw wikipedia and googled this but still don't get what this space is called.. I want to know (i)name, (ii)...
5
votes
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 ...
0
votes
3answers
3k views

WLOG means losing generality?

Isn't the use of "without loss of generality" in math proofs a bad formulation? To me it's sound similar as someone saying: "Without getting personal, I think you're jerk." I mean, when the writer ...
0
votes
3answers
132 views

Is there a name for expressions of the form $n^n$?

$n*n$ is a square number. Is there a corresponding descriptive term for $n^n$? Auto-power? 2nd-order tetration?
6
votes
2answers
1k views

How many classification of mathematical topics exists?

I found only one Mathematics Subject Classification, are there more?
3
votes
1answer
157 views

Motivation for the term “transitive” group action

I have two questions: In a text, I read that a group permutes pairs of faces of a solid transitively. Geometrically, what are they referring to, and what is an example of when a group may not ...
0
votes
1answer
327 views

Negatively Correlated Events

I showed the following inequality to a colleague, where $A$ and the $B_i$ are all events: $$ \Pr\left(A \mid \bigwedge_{i = 1}^n \overline{B_i} \right) \leq \Pr(A) $$ He summarized, "So $A$ is ...
4
votes
1answer
2k views

What is the difference between a function and a map? [duplicate]

Possible Duplicate: Is there any difference between mapping and function? I am an aspiring mathematician who just started out. What is the difference between a function and a map? Or are these ...
11
votes
3answers
364 views

Has this algebraic structure been named or studied?

Apologies if this is is not very well-defined or exposes my ignorance; I know comparatively little about abstract algebra. The structure of certain programming languages can be described with the ...
4
votes
1answer
221 views

What is WHSSETIT?

I am working through a 7 step statistical procedure for hypothesis testing. Step 7 has a field marked WHSSETIT?. What does this acronym stand for and what is the ...
2
votes
1answer
115 views

Definition of tautological action

What is the precise meaning of the term 'tautological action' as used for example in this Wikipedia page in the context of semigroup actions? For reference the particular sentence is: "A ...
0
votes
0answers
76 views

Abbreviations in Combinatorial Graph/Matrix theory

I'm getting started with research in combinatorics. I have come across a reference that uses a great deal of abbreviations. I was able to figure most of them out but there are a few that I can find. ...
7
votes
2answers
237 views

Extending a partial order to antichains

Let $(S, \leq)$ be a partial order. Let $T$ be the set of antichains of $S$ (i.e., subsets of $S$ whose elements are pairwise incomparable). Define a relation $\leq'$ on $T$ as follows: for all $A$, $...
0
votes
1answer
91 views

Anisotropic equations

Someone was giving a talk about modeling tumor growth in 3D, after which someone asked the question: "Are all of your equations anisotropic?" It sounded like he was referring to inclusion of unknown ...
3
votes
1answer
493 views

Difference between “measure on” and “measure over”

I want to make sure I understand the difference between the terms "measure on" and "measure over," assuming there is one. Is a measure on the set $X$ the same as a measure over its power set $\...
1
vote
2answers
48 views

Set $A$ and Set $B$ in each others closures

Let $A$ and $B$ be sets such that $A\subset \overline B$ and $B \subset \overline A$. Isn't that an equivalent statement to saying that $A$ is dense in the closure of $B$ and that $B$ is dense in ...
1
vote
1answer
58 views

Properly say superscripts locations

In english: $\bigl(x+y^2\bigr)$ is ('x' plus 'y' squared) $(x+y)^2$ is ('x' plus 'y' squared) How can I make the difference in english between the two?
4
votes
3answers
410 views

What is the difference between exponentials and powers?

I am a java programmer. But I have a doubt regarding a mathematics. There was a method called Math.exp(double a) description:Returns Euler's number e raised to the power of a double value. and another ...
7
votes
1answer
4k views

Why are vector spaces sometimes called linear spaces?

I have never come across the term 'linear space' as a synonym for 'vector space' and it seems from the book I am using (Linear Algebra by Kostrikin and Manin) that the term linear space is more ...