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

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-1
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1answer
20 views

Reporting what is seen about the maximum place of a function

I have plotted the $\sin$ function from $0$ to $5 \pi$. My problem is related to the report of what I see about the plot. I mean I don't know whether my reporting structure is correct or not!? ...
0
votes
1answer
27 views

Significant figures.

Calculate how many gram of p-nitrophenol you require to prepare 250 mL of a 11 mM solution. (Answer to 3 significant figures) I worked it out as $$250/1000 L * (11*10^{-3}\text{ M})$$ = $$2.75\times ...
0
votes
0answers
87 views

What is the exact meaning of self consistent?

I've heard the term self consistent being used when referring to differential equations, etc. but I have to admit that I'm unsure as to what is exactly meant by this. Is it simply that there is at ...
0
votes
1answer
32 views

About fibers and bijection

If $T = \{q\}$ consists of a single element of $B$, $f^{−1}(T)$ is called the fiber of $f$ over $q$. Thus a function $f : A \to B$ is a bijection if it has nonempty fibers over all elements of $B$ (...
0
votes
2answers
101 views

If algebraic is for algebra, _ is for calculus

Basically what I'm trying to find out if there's something called a "calculaic expression" or maybe "calculussic expression"? I mean if there are things called "algebraic expressions" for algebra, ...
2
votes
1answer
35 views

Functors which induce isomorphisms on isomorphism-sets

Is there a name for functors $F : \mathcal{C} \to \mathcal{D}$ with the property that for all $A,B \in \mathrm{Ob}(\mathcal{C})$ the map $F : \mathrm{Isom}(A,B) \to \mathrm{Isom}(F(A),F(B))$ is an ...
1
vote
1answer
176 views

What is a norm topology in functional analysis?

I am currently reading up about norm topology, I have a background in functional analysis but I do not know anything about topology, aside from that topology is a collection of open sets with some ...
1
vote
1answer
62 views

What does $x_n\rightharpoonup x_0$ mean?

What does $x_n\rightharpoonup x_0$ mean? It's hard to find what this means from the literature without knowing what it is a called. Is this weak convergence?
3
votes
1answer
81 views

Do rings like this one have a name: $\mathbb{Z}[\sqrt[3]{2}]$?

I'm studyng basic ring theory, in a "master's degree" in math. We've studied this objects in class: $\mathbb{Z}[\sqrt[3]{2}]$ and another one similar: $\mathbb{Z}[\sqrt[3]{2}, \sqrt{6}]$. The ...
0
votes
1answer
82 views

What is the word instead of “valley”

I have a plot as below, there is a "valley" in it. But I know the word valley is not suitable for my plot which has scientific details. What is the best word for describing the z component behavior ...
0
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0answers
32 views

Name for a particular type of set/set membership

This might be a philosophical rather than a mathematical distinction, but it there a name for a set whose members are selected on the basis of some property they hold, where the property is distinct ...
1
vote
1answer
17 views

What does discriminant of polinomial discriminate?

My understanding of the word when used in other contexts is to mean an object which classifies other objects into classes (possibly based on equivalence relation). But in what sense is discriminant ...
0
votes
1answer
50 views

Spanish translation for the term operad?

I would like to know which is the correct term in Spanish for operad(s)? https://en.wikipedia.org/wiki/Operad_theory I cannot be operador, since that is reserved for operators. I do not see anything ...
0
votes
1answer
150 views

What is this shape called?

I've encountered an unusual shape that I have no idea the name of. We have a sticker on the shape that tells us the equation $z^2 = \frac{x^2}{a^2-y^2}$ Here is a picture of the shape itself: http://...
3
votes
2answers
594 views

What is “pointwise”, in the context of function composition?

APOLOGY: This question is asked by someone foreign to math, with the expectation that math.stackexchange can be a resource to (among other things) understand math concepts. I'm a self-taught project-...
0
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0answers
35 views

How to define the following set?

I have a seemingly elementary question from Set nomenclature. If $B = \bigcup\limits_{i=1}^{\infty} A_{i}$ such that $A_i \subseteq {B}\;{\forall}\;i$, then does set $B$ have a special name, ...
4
votes
2answers
69 views

Conditions that topologies must have if (only if) the condition “$G_\delta$ iff (open or closed)” holds?

Consider the class of topological spaces $\langle X,\mathcal T\rangle$ such that the following are equivalent for $A\subseteq X$: $A$ is a $G_\delta$ set with respect to $\mathcal T$ $A\in\mathcal T$...
0
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0answers
13 views

Terminology for excluded nodes

Given the following tree: A / \ / \ B C / \ \ / \ \ D E F / \ / \ G H Regarding node ...
2
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0answers
31 views

How to name the branch of the Lambert W function?

The Lambert W function has two real branches: the principal branch and the secondary real branch: the former is denoted by $W_0$ or $W$, the latter by $W_{-1}$. How do we name them ? For example, we ...
2
votes
1answer
50 views

What does “canonical” mean in vector space?

I was watching this video: https://www.youtube.com/watch?v=RDkwklFGMfo And the professor is talking about the inner product... then he brings up the "canonical" representation of the inner product in ...
0
votes
0answers
26 views

Are There General Terms For Operands In An Equation?

I am curious if there are general terms for operands in any equation. For example, these are the terms for the basic operations: Addition: augend + addend = sum ...
-1
votes
1answer
57 views

Zorn Lemma, opposite ring and so on… [closed]

I just wanted to confirm some stuff with you regarding ideals, rings and the Zorn Lemma: Given that 1) A right ideal of any ring automatically is a left ideal of its opposite ring and 2) that ...
2
votes
1answer
71 views

What is the name of this solid?

You have a sphere. Take it and drill a hole along a diameter. You have a torus. Then rotate the sphere 90 degrees and drill along another diameter. There are now two perpendicular, intersecting ...
1
vote
0answers
22 views

Definition of exponential equation

What is a good definition of exponential equation? I'm trying to brush up on my calculus with Larson's "Calculus", and in one of the exercises he says that e^0=1 is an exponential equation. Shouldn't ...
1
vote
5answers
112 views

How do you explain that in $y=x^2$, y is proportional to the square of x?

My understanding is that all proportional relationships are linear relationships. If this is indeed the case, how is it that we can also say that in a non linear equation like $y = x^2$, y is ...
0
votes
0answers
27 views

Different ideal vs. dual lattice

I found this statement in a text trying to explain what the different ideal by Dedekind is: "The main idea needed to construct the different ideal is to do something in number fields that is ...
9
votes
1answer
127 views

Can any physical event “almost surely” not happen?

I asked a Question (Why do we say "almost surely" in Probability Theory??) about what exactly "almost surely" means and got some really good, helpful answers. The examples of events that ...
11
votes
3answers
883 views

Why do we say “almost surely” in Probability Theory?

I recently asked a Question and got a great answer that involved proving the "X is almost surely one of the roots of P". I know (now) that "almost surely" means "with probability 1", but I've never ...
1
vote
0answers
34 views

Why is there a need for other coordinate systems?

I have been wondering a lot about this. I have just reached A-Levels, and I have chosen the course Further Math. In class, we were talking about the Parallel coordinate system, but I didn't really see ...
2
votes
6answers
313 views

Why, in terms of the structure of proofs and proof strategy, is this proof of mine said to be backwards in logic?

Last year when I was doing the linear algebra and proof writing course, I was often said by my friends and my professors that the logical flow of my proofs are weird or even backwards. Recently, I ...
1
vote
0answers
80 views

Should this be called a torus segment or torus sector?

Is there an accepted term to refer to portions of a torus as represented in magenta and blue in the picture at the address below? http://news.povray.org/povray.binaries.images/attachment/%3C48dae480@...
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votes
3answers
219 views

Cool math theorem names/terms? [closed]

Does anyone know any other cool math theorem names/math terms besides the no-ghost theorem and the monstrous moonshine?
7
votes
4answers
2k views

Is zero a scalar?

Is zero considered a scalar? In other words, is $\begin{bmatrix}0\\0\\\end{bmatrix}$ a scalar multiple of $\begin{bmatrix}a\\b\\\end{bmatrix}$ where $a$ and $b$ are real numbers?
0
votes
1answer
110 views

Name of symbol of null set.

What is the name of the symbol we use for empty set? Difference in notation of phi and void set? I found that symbols that we use for both are different but I know the name phi only. Not know the name ...
0
votes
0answers
40 views

Is there an official term for “double monotonic”?

I want to describe function that is monotonic increasing/decreasing up to some point, and then is allowed to switch to be monotonic decreasing/increasing (the other direction). In other words, it "...
2
votes
2answers
120 views

What is the precise definition of the ambient space

For instance, what is the ambient space of a singleton $\{x\}$, where $x \in \mathbb{R}$? Can it be the singleton itself? $\mathbb{R}$? $\mathbb{R}^n$? or some arbitary set that happens to contain $\{...
1
vote
1answer
433 views

Can a arithmetic progression have a common difference of zero & a geometric progression have common ratio one?

How many three digit numbers have the property that their digits taken from left to right form an Arithmetic or Geometric Progression? Eg. 123 is in form a AP when the digits are taken from left to ...
0
votes
0answers
88 views

language: absolutely summable vs. absolutely convergent

I know what it means that a series is absolutely convergent. Now I faced the term absolutely summable and I am not sure how it is used correctly. In some sources I have found an explanation that it is ...
0
votes
1answer
49 views

Dedekind's “different”: sources, definition, original name

I am interested in getting the original information regarding Dedekind's idea of the "different" (regarding ideals). Particularly, I am interested in: 1- Knowing the original German name he used for ...
1
vote
1answer
27 views

A Question on a Possible Graph Theory Term

Let $G$ be a graph and $K_n$ denote the complete graph on $n$ vertices. Given $G$ with $n$ vertices, is there a special term given to the number of edges $G$ needs in order to be a complete graph $K_n$...
1
vote
1answer
43 views

What are the implications of the dual norm of a norm?

I was doing a series of questions proving that the dual norm of $l_p$ is $l_q$, where $p,q$ satisfies $\frac{1}{p} + \frac{1}{q} = 1$. I was able to prove this result but I do not see the point of ...
0
votes
1answer
81 views

Technical meaning of “profinite circle”

In a private exchange with a professional mathematician, I found the following statement: the "small etale topos" of a finite field is a "profinite circle", and thus looks like circle. Could anyone ...
0
votes
0answers
58 views

Is the norm ball a set or the boundary of a set?

Recall normed ball in $R^2$ under different norms is typically intuited as follows But looking at someone of the definition of normed ball it seems that it describes a closed set rather than the ...
7
votes
1answer
150 views

Sources of morality in mathematics

Long ago, I have heard one of my mathematic teachers claim several times that a result, a conjecture should hold "moralement" in French ("morally" in English). Since then, I have heard the same ...
24
votes
11answers
4k views

Why is Lebesgue so often spelled “Lebesque”?

Henri Lebesgue (1875-1941) was a French mathematician, best known for inventing the theory of measure and integration that bears his name. As far as I know, "Lebesgue" is the correct spelling of his ...
2
votes
1answer
280 views

What is “Ext” short for in “Ext Functor”? [duplicate]

Strangely, I've never heard Ext functors referred to by any other name, and so I'm not sure what "Ext" actually means. The only thing I can think of that "Ext" might stand for is "Exterior", which ...
12
votes
2answers
945 views

Who decides after whom a theorem or conjecture is named?

Who decides after whom a theorem is named? When someone discovers and proves a theorem, it is almost always named after that person. But how about when person A conjectures a theorem, and B proves it?...
3
votes
0answers
52 views

Is there a name for this property of a subset of a field?

Let $F$ be a field with the addition $(x,y) \mapsto x+y: F^{2} \to F$; let $A \subset F$ be nonempty; and let $(P)$ be this property of $A$: for every pair of $x,y \in A$ we have $x+y \notin A$. For ...
2
votes
0answers
53 views

Are the following conditions necessary and sufficient for the desired partial order isomorphism?

Before I get to my questions, let me clarify some terminology and notation that I will be using. $\DeclareMathOperator{\pr}{pr}$ $\DeclareMathOperator{\ext}{ext}$ $\DeclareMathOperator{\rank}{rank}$ $\...
0
votes
1answer
60 views

The use of English language in mathematics

My question is about the use of English language in mathematics. Should I write "Given a basis $b_n$ of the linear space $B_n := span\,b_n$..." or "Given a basis $b_n$ of a linear space $B_n := span\,...