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

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1answer
28 views

Compact set contained in the interior of another compact set

Let $X$ be a locally compact Hausdorff space. Does the property "every compact set is contained in the interior of some compact set" has a special widely known name? Is it related to paracompactness?
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1answer
56 views

What is the Fibonacci-like sequence called where one sums the last 3 numbers

The Fibonacci-sequence is defined like. $F_{x+1} = F_{x} + F_{x-1}; F_0 = 0, F_1=1, x \in {\Bbb N}$ Is there a special name for this sequence: $F_{x+1} = F_{x} + F_{x-1} + F_{x-2}$ ? Which?
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2answers
32 views

Why are Optional Stochastic Processes Important?

I understand to some degree why adapted processes, progressive processes, and predictable processes are important. EDIT: I am referring only to the continuous time case, NOT discrete time. But why do ...
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4answers
556 views

Why do they call it base 10?

Now, I know intuitively why it's called base 10: because there's 10 numbers. But see here's the thing, if we're working with numbers 0-9 (and of course we are), we use up our numerical artillery at 9....
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2answers
52 views

What is the sample space of a dice labelled with 1,2,2,3,3,3 for the standard dice?

When we roll a dice labelled with 1,2,2,3,3,3 for the standard dice. What is the sample space of this activity? If someone argues the probability of getting 1 is $\frac{1}{3}$. Because the person ...
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1answer
41 views

Term for a 'coefficient' used in multiple places.

Consider the case where I have a 'coefficient' $T$ such that: $f(x) = T(1 - e^{-x/T})$ What would you call this term? It's certainly being used as a 'coefficient', but its reciprocal is also being ...
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2answers
37 views

What is Convex about Locally Convex Spaces?

This might be a silly question, but what motivates the name "locally convex" for locally convex spaces? The definition in terms of semi-norms seems to have nothing to do with convexity or with the ...
1
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1answer
48 views

Product of sets as complexes

What does it mean to take the product of two sets of complex numbers as complexes? Reading this paper: "The Determinant of the Sum of Two Normal Matrices with Prescribed Eigenvalues" by N. Bebiano ...
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1answer
35 views

Terminology of “Random variable”

A random variable $X$ is a measurable function $X : \Omega \rightarrow E $ where $\Omega$ and $E$ are measurable sets. So, as far as I can see from this definition, random variables are just ...
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1answer
38 views

Inner, outer, tensor, cross product - where do the names come from

Well, I could imagine the reason for the latter - due to the convention to write the cross product as $\alpha_1 \times \alpha_2 \times \dots \times \alpha_n$. But for the others - where do their ...
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2answers
36 views

What is the difference between Mapping and Morphism

I wonder if there's differences between Mapping and Morphism. Although the terms are used in different context i.e. mapping for set theory and morphism for category theory, from my understanding they ...
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1answer
46 views

What is the difference between an adapted process and a predictable process?

As the footnote on page 1 of this document mentions, even most experts in the field of stochastic processes don't seem to know rigorously what the difference is. However, since I don't have any idea ...
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2answers
307 views

Is it bad to call series a generalization of sum?

In a recent question I asked why series has a name separate from that of sum, and the general answer was that a series does not have the nice properties of sum. Does this mean it is bad to call series ...
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3answers
1k views

Why is it called a series?

Why did we make a new name for infinite sum? Was something wrong with calling it an infinite sum, or is it highlighting a difference between finite and infinite?
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0answers
39 views

Is there a name for this measure?

For any given set $X$, define a measure $u$ on $\wp(X)$ where for all $A \in\wp( X)$: $$u(A)=0\text{ if }A\text{ is countable, and }u(A)=\infty\text{ otherwise}$$
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1answer
31 views

Name of a family of Coxeter groups

From the following image I know that the first of group is the symmetric group of rank $n$ and the second is known as the Hyperoctahedral group. I want to know if someone knows the name of the ...
0
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1answer
50 views

What is the meaning of (resp. closed) in set theory?

I'm sure this a spectacularly basic question but I can't seem to find the definition of this anywhere. Here's some context: If $U$ and $V$ are open (resp. closed) then $U\cup V$ is open (resp. $...
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1answer
36 views

Terminology: If $A, B$ are subspaces of $V$ and $A \cap B = \{0\}$ then they are …?

If $A, B$ are subspaces of $V$ and $A \cap B = \{0\}$ then ... If $V = A \oplus B$ they are complementary, otherwise I think that Halmos describes them as disjoint but this seems at odds with the ...
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0answers
41 views

The notation of 'greater than or equal to'.

I've known that the following marks are equal. However, both marks are used in the same book. I was wondering whether there is some difference between them.
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1answer
107 views

Why is the Topology of a Graph called a “Topology”?

The topology of a graph (i.e. a network topology), as far as I can tell, doesn't actually have anything to do with open or closed sets, nor does it have any consistent, rigorous definition in practice....
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0answers
17 views

What is the name of function, which codomain is a given set?

Is there a special short term for any function $F$ from the family of functions $F(A)$ for the given set $A$ so that $A$ is the codomain of any function $F \in F(A)$? For example, suppose we ...
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0answers
29 views

Why we name one side as the perpendicular of an angle but does not actually define it?

If I have a right angled triange: $\qquad \qquad \qquad \qquad$ I was wondering why we name the sides like this? The base of $A$ kind of make sense. But the perpendicular of $A$ what relation does it ...
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1answer
19 views

Definition of vertex-cut for digraph?

I am trying to understand vertex cut for digraph. I could find this for graphs Vertex cut is a vertex whose removal increases the number of components in a graph. (D67, Handbook of Graph Theory by ...
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1answer
79 views

What do you call such an object?

I would like to know if there is a name for an object $X$ in a (finitely complete and cocomplete) category $\mathcal{C}$ which has the following property: $X$ is non-empty and for every sub-object ...
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1answer
31 views

Definition of component for a digraph?

I could find this in Wikipedia Component: A connected component of a graph is a maximal connected subgraph. The term is also used for maximal subgraphs or subsets of a graph's vertices that have ...
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0answers
11 views

K-wise identical marginal distributions

Suppose I have two joint distributions described by the two sequences of random variables,$X_1, \ldots, X_n$; $Y_1, \ldots, Y_n$. Is there a name/theory/reference for when these two distributions ...
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3answers
85 views

What is the reason for naming a function odd or even [duplicate]

We say that a function is called odd if $$f(-x)=-f(x)\\ (1)$$ and a function is called even if $$f(-x)=f(x)\\\\\\ (2)$$ But why do we call them odd and even. It feels a very peculiar choice of ...
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2answers
30 views

Quantum group notation

I was jumping into the deep end and reading a few papers and lectures on quantum groups. My knowledge on Lie algebras is a bit thin but I was just wondering the notation used in the starting of this ...
0
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1answer
27 views

Is every decidable language accepted by a turing machine? [closed]

I am taking a cs class and the lecture slides are not very complete on this topic. can somebody clarify? thank you
0
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2answers
15 views

Name for opposing (complementary) multisets (bags)

I am looking for the accepted mathematical name for opposing multisets (or complementary multisets). I have done a Google search and a Stack Exchange search, and have come up empty. These are the ...
2
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2answers
44 views

Is the universal quantification symbol $\forall\;$ known as “for any x” or “for all x” in First Order Logic & why is this different to Discrete Math?

I'm reading a book by Mark Tarver called Logic, Proof and Computation. Chapter 8 (starting p71) is about First Order Logic. On page 77 (of Chapter 8) the author writes: For any value for 'x', in ...
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1answer
35 views

What is the meaning of “smeared limit cycle”?

I'm reading the paper Phase dynamics of coupled oscillators reconstructed from data by Kralemann et. al. (2008), which is about representing phenomena that exhibit a stable limit cycle (i.e. non-...
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5answers
2k views

What is an integer?

When we define an integer, we say it is a whole number that can be positive or negative or equivalently it is a number with no fractional part. Does that mean it is a number with no fractional part in ...
0
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1answer
32 views

Is there a classification for this kind of graph?

Is there a classification for a graph with the following properties? Finite. Directed. Every vertex points to some vertex. The third property necessitates the existence of at least one cycle. All "...
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2answers
2k views

Why are Boolean Algebras called “Algebras”?

Boolean algebras aren't algebras (to the best of my understanding). So why are they called algebras? Wouldn't it make more sense to call them a "Boolean system" or a "Boology" or something else like ...
2
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1answer
44 views

Conditional Distributions vs. Stochastic Processes

Is the concept of a version of a stochastic process related to the concept of a version of a conditional distribution? And is a regular version of a stochastic process somehow the same thing as the ...
1
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1answer
59 views

When to use $\in$ and $\subseteq$ when talking about bases and topologies

Can someone demonstrate a concrete example of when to use $\in$ and $\subseteq$ when talking about topologies and bases? When is something $\subset$ of a basis or a topology and when is something $\...
0
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1answer
41 views

Meaning of “$r \to s$ is a tautology” in the definition of “implication” and “equivalence”

What does it mean to say the following: $$ r \to s\ is\ a\ tautology$$ I make the following truth table: $$\begin{array}{ l c c r } r & s & \lnot r & r \to s \\ \hline T & T &...
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2answers
29 views

Genral solution vs Fundamental Solution to ODE. The Difference is?

I've been reading intros to ODE and the problem of terminology has overwhelmed me. As far as I understand: n-Parameter family of solutions to ODE is a solution in a form $c_1y_1+c_2y_2+...+c_ny_n$ ...
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4answers
86 views

An antonym for “converse”

Suppose you are proving $p \leftrightarrow q$. In your first paragraph you prove $p \rightarrow q$. Your second paragraph begins, “For the converse, assume $q$ holds.” In this situation, we have a ...
3
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3answers
220 views

Why does the name “epimorphism” refer to a surjective homorphism?

The wikipedia page talks about epimorphisms with category theory in mind, but I have no experience with this and ask this question from a group theory point of view (answers from any point of view are ...
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6answers
746 views

When can we not treat differentials as fractions? And when is it perfectly OK?

I am a first year calculus student so I would prefer if answers remained in Layman's terms. It is common knowledge and seems to me a mantra that I keep hearing over and over again to "not treat ...
5
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3answers
97 views

Whats the difference between a series and sequence?

I was looking at a question earlier that involved sequences and found out that the sequence converged to 0 but the series diverged to infinity. How is that possible? for example the sequence was $a_n$ ...
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2answers
65 views

Name of the union of a set with its holes

Given an arbitrary connected and compact set $S$ with holes in it, is there a name for the simply connected set formed by the union of $S$ and its holes? For example, let $S = \{x\in \mathbb{R}^n\ |\ ...
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2answers
41 views

A matrix of a single 1 in each row and 0 elsewhere

Is there a particular name given to a matrix of m rows and n columns such that it must have one and only one 1 in each row and 0 elsewhere? For instance: ...
0
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1answer
13 views

Is there a proper term for sets of interdependant functions?

I am looking for a term that would describe the sets of functions that are very closely related, such as: the trigonometric functions $\sin$ and $\cos$ the hyperbolic functions $\sinh$ and $\cosh$ ...
2
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1answer
32 views

Name of the modular group

I've been studying the hyperbolic plane and the action of the group $PSL(2,\mathbb{R})$ on it. I found that the modular group $PSL(2,\mathbb{Z})$ is a discrete subgroup of $PSL(2,\mathbb{R})$ so it's ...
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0answers
16 views

Is there a good term for pairs of related variables in a system?

(Non-mathematician here. Sorry). Suppose you have a problem with lots of unknowns. The problem allows many solutions (possibly infinite). Certain pairs of unknowns (you don't know which ones) ...
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1answer
29 views

What counts as a “Neighbor” in Conways' game of life?

I have looked everywhere but I cannot find an answer for this. Since I am bored, I am trying to create this game, but I can't seem to figure out what is considered a "Neighbor". Is it only directly ...
2
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1answer
38 views

What does the word “Comprehension” mean in the Axiom of Comprehension?

I understand roughly what the Axiom of Comprehension means, that any predicate can be used to construct a set of the elements that satisfy the predicate. But in English terms, where does the word "...