0
votes
0answers
30 views

The term $rank$ in methematics

Reading wikipedia's disambiguation page about the "rank" word I see many concept of rank of many different matematical object. I only know about the rank of a graded poset and the rank of a set that ...
2
votes
1answer
70 views

Definition of the $\sec$ function

I am a postgraduate student of mathematics from Slovenia (central Europe) with quite some experience in mathematics. While answering questions on this site, I often encounter the function $\sec(x)$ ...
2
votes
1answer
64 views

why calling these 'algebra' and 'ring' too?

In measure theory you have 'algebra's' and 'rings' as subsets of the powerset of the underlying set of the measurable space. If I am well informed then you speak of an algebra if it is closed under ...
2
votes
0answers
39 views

Replacing $q^2$ by $q$

I have a rather strange question. Suppose we are given a formal power series $$S(q^2) = \sum_{n = 0}^\infty a_n q^{2n}.$$ I wish to replace $q^2$ by $q$. This implies that $S(q) = \sum_{n = 0}^\infty ...
3
votes
1answer
55 views

Why is a perfect group called a perfect group

A group is called perfect if we have $[G,G]=G$. I was wondering in what sense is this group perfect? I've never really done anything much with perfect groups so I don't really know anything about ...
1
vote
1answer
36 views

The Jacobi nome $q$

Does anyone know why $q = e^{-\pi K'/K} = e^{\pi i \tau}$ is called the nome? Is there a historical reason? Does the word nome mean something in Latin or German?
1
vote
0answers
11 views

Is there a specific term for such collections of filters?

Let $U$ be a set. Concept = "a set $\mathscr{C}$ of proper filters on $U$ such that if $X\in\mathscr{C}$ and $Y$ is a proper filter on $U$ and $Y\supseteq X$, then $Y\in\mathscr{C}$." Is there a ...
2
votes
2answers
66 views

Why are left/right adjoint functors not called up/down?

I am studying category theory and I recently learned about adjoint pairs of functors. It seems to me that they are called left and right adjoints because if we have categories $\mathcal{C}$ and ...
2
votes
1answer
33 views

Why do we want to define a $k$-scheme to be birational if the rational map (and its inverse) to $\Bbb A_k^n$ is over $k$?

Two varieties $X,Y$ are said to be birational if there exist rational maps in each direction such that either composition is the identity on a open dense subset. Note that here the morphisms aren't ...
4
votes
1answer
68 views

Have arrows in a category with this property a special name?

Studying posets I encountered the notation $a\prec b$. It means that $a<b$ and no $c$ exists with $a<c<b$. If $a\prec b$ then in words $a$ is covered by $b$. Looking at a poset $P$ as a ...
3
votes
2answers
101 views

Definition: Theorem, Lemma, Proposition, Conjecture and Principle etc.

Definition: Theorem, Lemma, Proposition, Corollary, Postulate, Statement, Fact, Observation, Expression, Fact, Property, Conjecture and Principle Most of the time a mathematical statement is ...
0
votes
2answers
99 views

Growth Rate. A precise definition.

Recently I came across a problem (see statement below) growth rate . During my attempts to solve the exercise I concluded that I do not know the meaning of need backup growth rate when this rate is ...
7
votes
3answers
521 views

Why are compact sets called “compact” in topology?

Given a topological space $X$ and a subset of it $S$, $S$ is compact iff for every open cover of $S$, there is a finite subcover of $S$. Just curiosity: I've done some search in Internet why compact ...
0
votes
1answer
35 views

Adding together curves or shapes to approximate something more complex

I'm looking for proper terminology / references for the following sort of problem: Say we have some one-dimensional curve like $y = 10$ defined over the real valued domain $[0,1]$, and we ask, how ...
1
vote
1answer
77 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
1
vote
1answer
63 views

What is matrix inequality such as $A>0$ or $A\succ 0$?

I am trying to gather here different meanings of the same symbol, inequality symbol or the succ symbol. I find many other use them so many different ways. Sometimes, $A>0$ means $\bar x^T A \bar x ...
0
votes
0answers
44 views

What does the sentence “every element of $S$ has a unique colour” mean?

Does the statement mean that each element of $S$ has exactly one colour, or that no two elements of $S$ share the same colour? Or could either interpretation be valid, depending on the context?
3
votes
0answers
72 views

Etymology of the term “weight vector”

I am writing a work on the representation theory of $SU(3)$ in basque and I would like to know the etymology of the term $\textbf{weight vector}$ in order to properly translate it.
4
votes
3answers
939 views

What does it mean to solve a math problem analytically?

I'm reading a Calculus book for my own edification and at the beginning the pre-calculus introduction has the problem, $3x+y=7$ They talk about solving the problem graphically, analytically, and ...
0
votes
1answer
87 views

How to make a ghost manifold [closed]

How does one mathematically define a manifold that can pass through another manifold? A "ghost" passing through a "wall" type construction. I understand that this may be done by creating a copy of the ...
0
votes
1answer
43 views

We refer to X for standard notations and definitions from Y

I'm having problems with my mathematical English, so I'd like to ask for your help! Is it correct to write something like "Unless stated otherwise, we refer to [1] and [2], respectively, for standard ...
1
vote
1answer
55 views

Additive analogy of proportionality symbol

The relation of proportionality is quite abundant, and so for convenience there exist symbols, such as "$\propto$", to denote it. I would like to know if there is likewise a symbol to denote the ...
5
votes
2answers
193 views

Is $(-\infty,\infty)$ a closed **interval**?

Note that we are working in the reals, not the extended reals. Do you understand a closed interval as "an interval that is a closed set" or as "an interval that includes both its endpoints"? If the ...
2
votes
0answers
29 views

Soft question on “what” vs “which” when referring to sets of numbers [closed]

Maybe this question is completely inappropriate for this forum. I therefore apologize in advance and welcome anyone to close it should this be the case. When referring to elements of sets, should you ...
1
vote
1answer
94 views

Is there a way to mathematically describe “surprise”?

Let's say that there are ten people entered into a random drawing, the winner gets some large prize. If I were one of those ten people, and I were to win, then I would be pleasantly surprised. If ...
9
votes
1answer
332 views

On a joke of Yoneda embedding

I have heard a joke like this: The Yoda embedding, contravariant it is. And a joke concerning "How to put an elephant into a refrigerator", a comment from "Category Theorist" says Isn’t this ...
25
votes
2answers
927 views

Word origin / meaning of 'kernel' in linear algebra

It may be the dumbest question ever asked on math.SE, but... Given a real matrix $\mathbf A\in\mathbb R^{m\times n}$, the column space is defined as $$C(\mathbf A) = \{\mathbf A \mathbf x : ...
0
votes
1answer
38 views

Optimum equals extremum?

Is there any difference between optimum and extremum? It seems to me that they are the same. Am I right?
6
votes
0answers
57 views

Analogue of the term 'summand' for unions and intersections.

If we have a sum $\sum_{i=1}^na_i$, we call the terms $a_i$ summands. In fact, in the cases of addition, subtraction, multiplication, and division, we have a large vocabulary to describe the various ...
4
votes
1answer
125 views

Why is “Amenable Group” a pun?

"The original definition, in terms of a finitely additive invariant measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in ...
3
votes
1answer
248 views

What does “rigor” mean in mathematics? [duplicate]

I spend a lot of time on math.se and even though I don't understand many of the questions posed, I try to understand what is being said or atleast wiki something to get some gist of the question and ...
6
votes
1answer
114 views

Who introduced the term “norm” into mathematics?

I've always been curious about the motivation behind the use of the word norm, as used in linear algebra and functional analysis, for a function that assigns a positive number to a vector. Who ...
1
vote
1answer
49 views

Recursive application of a function : Symbol of [duplicate]

I need to apply a function $f(x)$ recursively/repeatedly for n times; how do I express it (mathematically) ? Is their a mathematical symbol which denotes $f(x)$ applied n times ie $g(x,n)$ ...
0
votes
1answer
30 views

What is the difference between “model” and “method”

I am not sure which forum to ask this question since the answer may change depending on the scientific area. I am analysing some time series using linear regression. I predict data using the linear ...
3
votes
2answers
121 views

What's the correct name in english for “Analysis in $\Bbb R^n$”?

Well, this question may seem silly and I fear it's even out of topic here. My motivation to ask that is to know the correct terminology when talking about that here in Math.SE. The point is, here in ...
4
votes
1answer
70 views

Who introduced the term Homeomorphism?

Who introduced the term Homeomorphism? I was wondering about asking this question on english.stackexchange but I think this term is strongly (and maybe solely) related to mathematics.
3
votes
1answer
130 views

Name for three-valued sign $+, -, 0$

Is there an accepted term (an adjective or prefix) like strict, trichotomous, strong or definite sign to indicate the three-valued sign whose values are $+$, $-$, and $0$? Are there words reserved ...
12
votes
6answers
347 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
1answer
35 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., ...
6
votes
4answers
380 views

Are there rules in the useage of prepositions in Math?

It is often to use prepositions in various expressions. E.g. $2$ is in the set of natural numbers $\mathbb N$ The symmetric group on 3 letters $S_3$ is the group consisting of all possible ...
1
vote
1answer
102 views

Correct way of saying that some value depends on another value x only by a function of x

I would like to know what good and valid ways there are to say (in words) that some value f(x), which depends on a variable x, in fact only depends on x "through" some function of x. Example: For ...
3
votes
3answers
214 views

Zorn's Lemma $\equiv$ Axiom of Choice

I'm confused a little bit about this, I've been told many times that Zorn's lemma is equivalent to the axiom of choice. Is it an axiom or is it lemma, I mean is there a proof of Zorn's lemma or we ...
15
votes
5answers
2k views

Is 'no solution' the same as 'undefined'?

Today in class my teacher wrote something along the lines of: $6^x = 0$ And proceed to heed a response from the class. A few people shouted undefined. So the teacher then writes: no solution ...
4
votes
2answers
121 views

Does this problem have a name?

Recently our lecturer told us that it is an unsolved mathematical problem if the following while loop aka iteration ever terminates. Unfortunately I forgot to ask him what it is called. If someone ...
5
votes
5answers
384 views

What exactly is “approximation”?

There are a lot of great "approximations" that exist in the mathematical field:$$\dfrac{22}{7} \approx \pi$$ $$e \approx \left(1 + \dfrac{1}{n}\right)^n$$But the fact that I have yet to know what ...
0
votes
1answer
140 views

What other rules are there in mathematics?

I'm reading Conceptual Mathematics: A First Introduction to Categories. a set $A$, called the domain of the map; a set $B$, called the codomain of the map; a rule assigning to each element ...
4
votes
2answers
94 views

Why saying that “$x$ is an indeterminate real number” is misleading?

I'm reading: Behnke's Fundamentals of Mathematics, Vol.1 On page 23, he says: In order to indicate that a variable $x$ has the real numbers for its range, mathematicians often say that $x$ is ...
3
votes
1answer
122 views

What does arithmetic actually mean (as an adjective)

Ok so I've seen the adjective 'arithmetic' (stress on the e) bandied about from time to time in reference to the "arithmetic theory of some subject" (elliptic curves for instance), or the "arithmetic ...
8
votes
3answers
2k views

Difference between “intercept” and “intersect”

What is the difference between intercept and intersect? Can they be used interchangeably? For example, intersecting lines and intercepting lines.
4
votes
2answers
402 views

The usage of ad hoc vs a priori in mathematical papers

I was reading the paper Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems, where the author phrased something as this: The analyses of these methods are ad hoc but ...