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

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4
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1answer
191 views

Terminology: Difference between Lemma, Theorem, Definition, Hypothesis, Postulate and a Proposition

Based on observation after reading few books and papers, I think that Lemma : Lemma contains some information that is commonly used to support a theorem. So, a Lemma introduces a Theorem and comes ...
0
votes
0answers
54 views

What is the name of the group $\mathbb Z_2\times \mathbb Z_2\times \mathbb Z_2$?

I know, that $\mathbb Z_2\times \mathbb Z_2$ is the Klein four-group. Is there a nice name for $\mathbb Z_2\times \mathbb Z_2\times \mathbb Z_2$ too?
2
votes
2answers
31 views

Does “sphere” denote the surface or the entirety of a solid ball?

In everyday English, the word "sphere" denotes a 3-dimensional object, including the points inside the surface and its center. However, I get the sense that in mathematics, the sphere is used ...
1
vote
1answer
30 views

How to read $\frac{dy}{dx} $ when the term is only given?

When the term $\frac{dy}{dx}$ (not $\frac{d}{dx}y$) is only given, how to read the term between "the derivative $y$ with respect to $x$" and "the quotient of the differential $dy$ by the differential ...
1
vote
1answer
31 views

Is there another name for a vector?

I am writing a program uses contains both vectors (direction and magnitude) and vectors (a matrix with one row/column) and my head is spinning. I could replace the latter kind of vector with ...
-2
votes
4answers
531 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 ...
0
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0answers
13 views

Terminology for property of two branches of a tree

Consider a tree $T$. A branch $B$ of a tree $T$ is just a proper subtree of $T$ (that is a subtree $B \subset T$ and $B \neq T$). Lets consider $B_1$ and $B_2$, two branches of a tree such that $B_1$ ...
1
vote
1answer
38 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 ...
1
vote
3answers
58 views

I don't get it, does “augmented chain complex” actually mean anything?

If I understand correctly, chain complexes make sense in any category enriched in the world of pointed sets. In practice, there's also a notion of an augmented chain complex, where we have an extra ...
4
votes
3answers
46 views

Vectors sometimes used in math just as arrays/lists of numbers, sometimes as concept of “change”

As a freshman in a small town college. Ive been getting mixed signals to what vectors (and matrices/tensors) are. Sometimes I get the feeling they are used just as containers/arrays for multiple ...
0
votes
2answers
6k views

What is the difference between an identity, an equation and a conditional equation?

What is the difference between an identity, an equation and a conditional equation? Thank you?
0
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0answers
11 views

name/term for the property of non-analytic complex functions causing “anisotropy”

I'm looking for a mathematical term here so I can understand the consequences of nonlinearity in a system of interest to me. Here's an example system that exhibits this behavior: $$ f(z) = ...
0
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2answers
31 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 ...
1
vote
1answer
51 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?
0
votes
0answers
16 views

What is the point of solving a system of linear equations using back-substitution (as opposed to reduced echelon form)

In lecture the other day, my professor offhandedly mentioned the existence of a process called back-substitution a way in which a computer program would solve a system of linear equations rather ...
0
votes
1answer
14 views

Monoid operation order sensitive?

It is a basic question, none the less I cannot find an answer: A monoid is associative (with an identity) (m1∙m2)∙m3=m1∙(m2∙m3). e∙m=m∙e=m If you consider a monoid over natural numbers (N,+,0) for ...
1
vote
1answer
24 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?
0
votes
2answers
49 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 ...
1
vote
1answer
40 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 ...
5
votes
3answers
93 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 $a_n$ ...
1
vote
2answers
35 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 ...
0
votes
1answer
37 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 ...
0
votes
1answer
32 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 ...
1
vote
2answers
30 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 ...
2
votes
1answer
35 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 ...
6
votes
2answers
298 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 ...
11
votes
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?
14
votes
2answers
189 views

The term “elliptic”

There are many things which are called “elliptic” in various branches of mathematics: Elliptic curves Elliptic functions Elliptic geometry Elliptic hyperboloid Elliptic integral Elliptic modulus ...
2
votes
1answer
27 views

Term for maximal proper divisors

What do you call a divisor, $d$, of a number $n$ which is of the form $d = n/p$ where $p$ is a prime divisor of $n$? For a cryptography class I need to discuss such numbers (to describe how to find ...
1
vote
1answer
41 views

Terminology for functions with $F(a,a,\dots,a) = a$

Is there a commonly used terminology for functions $F : \mathbb{R}^n \rightarrow \mathbb{R}$ such that if $x \in \mathbb{R}^n$ and $x_i = a$ for all $i\in \{1,\dots, n\}$, $F(x) = a$ ?
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0answers
24 views

Rewording the definition of closure

In Munkres there was a statement: Given a topological space $(X, \tau)$ $x \in \overline A \iff \text{ for every open set } U \text{ containing } x, U \cap A \neq \varnothing$ Following from ...
2
votes
1answer
254 views

What is the origin of the (nearly obsolete) term “binary decimal”?

What is the origin of the (nearly obsolete) term "binary decimal"? At least two important publications in the 1930s used this oxymoron to mean what is now ...
1
vote
0answers
37 views

Is there a name for this measure?

For any given set $X$, define a measure $u$ on $\wp(X)$ where for all $A \in\wp( X)$: $$u(A)=0\text{ if }A\text{ is countable, and }u(A)=\infty\text{ otherwise}$$
1
vote
1answer
30 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
votes
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. ...
0
votes
2answers
485 views

Math terminology: What are rules regarding hyphens? (Nonzero vs. non-zero)

This question is geared toward clarifying terminology in writing math. Which terms are correct and why? A set $E$ is non-empty. A set $E$ is nonempty. The number $x$ is non-negative. The ...
0
votes
1answer
76 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 ...
0
votes
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 ...
5
votes
1answer
73 views

Are the terms 'clan' and 'tribe' common in mathematics?

In the book 'Vector Measures' by Dinculeanu, he starts the discussion by talking about "classes of sets", and introduces two pieces of terminology I've never seen before, and can't find any evidence ...
12
votes
1answer
94 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 ...
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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.
0
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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 ...
2
votes
2answers
751 views

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it? Thanks.
0
votes
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 ...
2
votes
1answer
28 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 ...
0
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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 ...
0
votes
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 ...
4
votes
3answers
84 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 ...
1
vote
2answers
29 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
votes
1answer
21 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