Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.
1
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2answers
61 views
Why the terms “unit” and “irreducible”?
I'm trying to understand why in a ring we choose the names unit to an invertible element and irreducible element in this definition
Maybe historical reasons?
For example, I suppose the second ...
1
vote
3answers
65 views
“Set of all formal products” - what does this mean?
List the set of all formal products of $(1+x^2+x^4)^2(1+x+x^2)^2$ with exponents summing to $4$.
What is this question asking exactly? What is a "formal product"? Does it have anything to do with ...
1
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2answers
32 views
Is there any specific terminology to refer to an initial sequence of a sequence?
Lets say you have a sequence $S = (0, 1, 2, 3, 4, 5, 6, 7, 8)$
And another sequence $T = (0, 1, 2, 3)$
Is there any specific mathematical term that defines the relationship between $S$ and $T$, ...
6
votes
1answer
115 views
Is “cofunctor” an accepted term for contravariant functors?
People are used to the prefix co- flipping arrows in a concept1, and I have seen people using cofunctor to mean a functor that flips arrows, i.e. that takes $A \to B$ to $FB \to FA$. I know this ...
0
votes
2answers
53 views
Definition of metastability
I was reading Terence Tao's blog post on analogies between soft and hard analysis when I saw that the soft analysis statement "$x_n$ is convergent" corresponds to the hard analysis statement "$x_n$ is ...
2
votes
1answer
96 views
What is the reason for the name *left* coset?
Let $G$ be a group and let $H \leq G$ be a subgroup. It seems that it is now standard to call the cosets
$$gH=\{gh \ | h \in H \}$$ the left cosets of $H$ in $G$. I have to admit to being slightly ...
1
vote
2answers
22 views
Terminology for an element of a partition?
Suppose I'm dividing some region $\Theta \in \mathbb{R}^n$ into subregions $\theta_i, i=1,2,3$ such that $\theta_i \cap \theta_j = \varnothing, i\ne j$ and $\cup_i \theta_i = \Theta$. I might say ...
2
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1answer
53 views
What is a hypersingular integral kernel?
While reading literature about boundary element and finite element methods I have repeatedly seen that some integral kernels are singular and others are hypersingular. Could you explain what is the ...
3
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2answers
57 views
Is there a difference between 'inconsistent', 'contrary', and 'contradictory'
Is there a difference between 'inconsistent' 'contrary' and 'contradictory'? As far as I understand, two statements are inconsistent when they can not both be true; two statements are contradictory ...
0
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0answers
40 views
What is that type of TSP
I'm searching for the name of the TSP-like problem.
The basic principal is like it follows:
When a city is visited by the salesman, he will came in one point and exit the city in another. The ...
7
votes
1answer
81 views
Is there a name for relations with this property?
Is there a name for relations $\rho : X \rightarrow Y$ such that for all $x,x' \in X$ and all $y,y' \in Y$ we have that the following conditions $$xy \in \rho$$ $$x'y \in \rho$$ $$xy' \in \rho$$ imply ...
2
votes
1answer
45 views
Substitution - what's the technical name of the inference rule?
Suppose the following are written down in some context.
$$3x^2 < y$$
$$x^2=xy-1$$
Then we may deduce (also within that context) that
$$3(xy-1) < y$$
What is the technical name of this ...
1
vote
2answers
36 views
Is it ever proper to say that the limit of a function equals infinity?
If I calculate a limit and get the value $\infty$, what is the proper way to communicate this? Can I say that the $\lim_{n\to\infty}a_n=\infty$ and therefore the sequence $\{a_n\}$ diverges, or do I ...
3
votes
0answers
29 views
“Disjoint” elements of a lattice - what's the correct terminology?
Given a set $X$ and a pair of subsets thereof, call them $A$ and $B$, we say that $A$ and $B$ are disjoint iff $A \cap B = \emptyset$. This generalizes to lattices with a least element. Given such a ...
9
votes
6answers
226 views
Should every group be a monoid, or should no group be a monoid?
Question: What is more convenient/useful? Writing mathematics as if every group is a monoid, or as if these two classes are disjoint?
Additional discussion. Define a monoid as follows.
Defn 1. A ...
2
votes
0answers
44 views
Terminology questions about a game where one may “save his progress” at the cost of a turn.
The game is for $p$ players who each start at square $1$. Each turn, a player can either roll an $m$-sided dice or place a marker on his current square. If he rolls $x\in\{2,\ldots, m\}$, he ...
3
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0answers
41 views
What's the mathematical field called where functions create and delete functions?
Motivation
In the field of modular, reconfigurable robotics there are some groups which use term rewriting, or specifically graph rewriting to describe the reconfiguration process of the modular ...
1
vote
5answers
76 views
How do I find the image of the functions $y=2$ and $y = 2x - 6$?
The function is $y=2$, the domain is just 2? And the image of it?
I don't think I quiet understand what the image of a function means, the domain is all values that it can assume, correct?
Could you ...
0
votes
0answers
33 views
Notation: Historic and Modern
I was just curious to find out if anybody here knows of a resource (online, text, whatever) that has a list of the various names of objects, functions, ideas, etc. in mathematics that have accumulated ...
2
votes
0answers
36 views
Semi-orbital equivalence relation
Edit: I was in kind of a hurry when writing this post and made a mistake in the formula defining $G_E$. What I had written said that $G_E$ preserves the set of classes of $E$, while I meant actually ...
2
votes
1answer
89 views
What does “Hauptidealsatz” mean in “Krull's Hauptidealsatz”?
What does "Hauptidealsatz" mean in "Krull's Hauptidealsatz"? Thank you very much.
0
votes
0answers
34 views
dimension of an ideal (definition)
Let $A$ be a commutative ring and $I$ an ideal. When we refer to the "dimension" of $I$, what exactly do we mean? Is it the Krull dimension of $A/I$? In particular, i am trying to understand the ...
5
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2answers
80 views
Does this qualify as a statement?
Is this a statement?
All positive integers with negative squares are prime.
What do we need to qualify as such?
-4
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3answers
122 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, ...
0
votes
1answer
15 views
What is the proper term for this kind of aggregation?
I have a bunch of values, which I aggregate as follows:
Order them from worst to best (whatever this means). The visual image is that of a horizontal line and the worst item is to the left of the ...
3
votes
2answers
77 views
Classes and Sets
Why are equivalence classes called so and not equivalence sets?
I am kind of not able to find the difference between a class and a set. What properties that a set have that a class cannot have? It ...
2
votes
2answers
67 views
How to interpret “rank” of a matrix intuitively?
What is the physical interpretation of "rank" of a matrix ? Why is it called "rank" ?
4
votes
1answer
65 views
Terminology for infinite groups, all of whose subgroup have finite index.
Is there a name for (infinite) groups such that every non-trivial, proper subgroup has finite index (e.g. $\mathbb{Z}$)?
0
votes
0answers
25 views
Weak Precedence Grammar and Bottom-up parsing
I am studying parsing, i.e. bottom-up parsing. it is said that there some rules which are used by weak precedence grammar. What does weak precedence grammar mean? What about precedence relation?
Any ...
1
vote
1answer
17 views
authority distribution and hub distribution
I want to understand the concepts authority distribution and hub distribution. As I see in gephi software, Authority measures how valuable information stored at that node is. Hub measure the quality ...
0
votes
0answers
25 views
What is the reason of the naming of the “simplex method”?
What is the reason of the naming of the "simplex method"?
Is there any method other than simplex? Or it has any other cause?
1
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2answers
34 views
Confusing with the concept of normalizer $N_G(H)$
I'm Confusing with the concept of normalizer $N_G(H)$.
It's a stupid question, sorry I'm new in this subject.
Following the Hungerford's concept:
If $H$ acts by conjugation on the set $S$ of all ...
2
votes
2answers
65 views
What to call $x^{-1}ax$?
If $G$ is a group and $a,x\in G$, then would we call $x^{-1}ax$ a conjugate of $x$ or a conjugate of $a$?
Sorry for such a short question, was just doing a problem and want to call this something so ...
5
votes
1answer
53 views
Inherited topology of logical Stone's spaces.
I'm asking here if the following construction is of any interest. I can not find any reference for that kind of thing, so either the subject is completely trivial, either I just don't have the correct ...
1
vote
1answer
33 views
Definition of correspondence
A one-to-one correspondence is an alternative name for a bijection between two sets, but to what does the term 'correspondence' alone refer? As far as I can see, it seems to be another term for ...
1
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1answer
27 views
In statistics, dispersion denotes how stretched or squeezed a distribution is, but what is the formal definition?
In statistics, dispersion denotes how stretched or squeezed a distribution is, but what is the formal definition by mathematical properties?
1
vote
1answer
39 views
Limit of a seqence $\{f_n \}_{n\in \mathbb N}$ of functions?
I don't really know how mathematicians talk about this concept.
I try to explain better what I mean with limit of a sequence of functions:
Given a countable set of functions $\{f_n \}_{n\in \mathbb ...
1
vote
1answer
41 views
What is the modulus of a number?
What is the exact definition of the modulus of a number? As far as I know, it is the distance between the origin and the point associated with this number. So if $z=a+bi \in \Bbb ...
0
votes
1answer
41 views
Sub-(complete lattice)? - what's the correct terminology?
Let $X$ denote a set, let $\mathcal{O}$ denote the open sets of a topological space with carrier $X$, and let $\mathcal{P}$ denote the powerset of $X$. Furthermore, let $\leq_\mathcal{O}$ denote the ...
1
vote
2answers
26 views
Independent and Dependent Variable Meaning?
Given a differential equation, for example:
$\displaystyle \frac{d^2x}{dt^2} + a \frac{dx}{dt} + kx = 0$
Is there a reason why we call $x$ the dependent variable and $t$ the independent ...
2
votes
1answer
30 views
Which expressions in English should I use for a morphism having a certain source and target?
Say that $f: A \rightarrow B$ is an arrow in a category $\mathcal C$. Which verbs or expressions do we use to express in an alternative way that $A$ is the source of $f$ and $B$ its target? E.g., ...
2
votes
2answers
60 views
the phrase “its derivative” when a function has a derivative only almost everywhere
Theorem: A function $F$ is an indefinite integral if and only if it is absolutely continuous
Corollary: Every absolutely continuous function is the indefinite integral of its derivative.
(thm ...
3
votes
0answers
59 views
Difference between elementary submodel and elementary substructure
This is a really "elementary" question, forgive the pun.
What is the difference between an elementary submodel and an elementary substructure (in first-order Logic)?
Sincere thanks for help.
2
votes
1answer
44 views
Properties which are constant on conjugacy classes of a group
Let $\Phi$ be some property which might hold of an element of a group, and say that in every group, $\Phi$ holds for some element $x$ of the group if and only if it holds for all the conjugates ...
3
votes
1answer
51 views
If monic, then *property*. Does the converse hold?
Theorem. Suppose $f : X \rightarrow Y$ is monic. Then for all $g : \bar{X} \rightarrow Y$ there exists at most one $h : \bar{X} \rightarrow X$ such that $f \circ h = g$.
Question. Does the converse ...
3
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1answer
43 views
Statistical Freedom
What is the English counterpart of the French term "statistique libre"?
The following excerpt, translated by me from an excellent 70's French textbook in mathematical statistics ([BAR]), defines the ...
2
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2answers
36 views
Name of the order with irreflexivity, antisymmetry and transitivity?
I have an order otherwise poset aka partial order but it is irreflexive so relationships such as 1R1 and 2R2 are impossible. What is the name of this order?
0
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1answer
36 views
A “Linear” Mapping - What am I talking about?
My situation:
I have a fixed initial state $|\psi_i \rangle$ which is a ($1 \times n$) column vector. I apply a linear operator $\hat{A}(\phi_{1,2,3,...,x})$, which has a number of variables, to ...
5
votes
2answers
65 views
Difference between root, zero and solution.
Can somebody precisely tell me what is the difference between a root, a zero and solution ?
Is it correct to say that an equation has solutions, and a polynomial has zeros or roots?
1
vote
4answers
48 views
Birthday paradox: meaning of random
In the wikipedia page (http://en.wikipedia.org/wiki/Birthday_problem) on birthday paradox the following statement has been said : "the probability that, in a set of $n$ "randomly chosen" people, some ...
