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

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54 views

Mathematical structures with name reffering to a country

I am looking for a list of mathematical structures (not theorems) that refer to a country or nationality. I only know of Polish spaces and Polish groups. Does anyone have other examples? Note: many ...
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1answer
46 views

Why did mathematicians name a functional that assigns number to function as a “distribution”?

Why did people name it as a "distribution"? I don't see the reason. My instructor told us don't bother with this strange name, but I guess maybe I will have a better understanding if I know the ...
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0answers
25 views

Terminology: order vs. degree (in general)

The word degree comes from Latin degradus (through French), which means something like step down. The word order comes from Latin ...
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5answers
535 views

Is there an intuitive, not-too-mathematical way of thinking about limit points? [duplicate]

so I know this question has been asked sooo many times. But I just have a few questions in particular, which despite searching, I haven't found an answer to. I appreciate any help. Book's definition: ...
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4answers
108 views

Is the logarithm of $\aleph_0$ infinite?

In classical mathematics $2^{\aleph_0}=\aleph_1$, right? So if $2^x=\aleph_0$, what does $x$ equal? In other words, can we define a logarithm for $\aleph_0$, and what should it be. Is it infinite? ...
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2answers
25 views

Comparing Open Bases and Covers

In Topology, I see a resemblance and similarity between open bases and open covers. Although this is a short question, what is the defining difference between the two that sets them apart? ...
2
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0answers
35 views

Rings where action of automorphisms on maximal ideals is transitive

If $R$ is a commutative ring, $\alpha: R \to R$ an automorphism of $R$, and $M$ a maximal ideal of $R$, then $\alpha(M)$ is also a maximal ideal of $R$ with the same quotient field. So the group of ...
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2answers
27 views

Does a one-to-one function exhibit “injectiveness” or “injectivity”?

I'm preparing some tutorials for students and I'm faced with writer's block. If I want to say a function is injective/one-to-one, would the function demonstrate "injectivity" or "injectiveness"? ...
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0answers
39 views

What's the word for a number which is used to scale down a value?

I'm a programmer and I'm creating an API in which there is a parameter the user can pass in which scales down a value. So for example: ...
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0answers
78 views

Mathematical definition of the Hamiltonian function.

I'm reading this nice text on Calculus of Variations, by Peter Olver. In page $8$, he calls $$J[u] = \int_a^b L(x,u,u')\,{\rm d}x$$ the objective functional, and the integrand $L(x,u,u')$ the ...
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22 views

Does the differential operator in the heat equation have a name?

Does the operator $$\frac {\partial}{\partial t} - k\nabla^2$$ have a name?
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1answer
52 views

Is there a name for this curve? Or, how should I describe the behavior of this graph (in words)?

I simulated some results that look like this: but I don't want to include the plot (my advisor is keeping me to a strict limit on figures and these are minor intermediate results). Is there a name ...
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1answer
52 views

“Quotient” as a verb

People here do use "quotient" as a verb: I searched for "quotienting" and got 12,890 results. [Edit: It's not as bad as I thought. Apparently I didn't understand how the search function works. When I ...
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1answer
65 views

Where can I learn to define mathematical terms?

For example, take the following: The radian measure of a central angle of a circle is defined as the ratio of the length of the arc the angle subtends, s, divided by the radius of the circle, ...
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1answer
63 views

Why are nodes and nodal sets called this way?

Nodes of standing waves are points where they are zero. Generally, nodal sets of Laplacian eigenfunctions are the sets of points where they are zero. Why is this the name for them (that is, why is ...
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0answers
32 views

A name for a particular covering map?

The quotient space of $\mathbb C$ obtained by identifying points differing by a Gaussian integer is topologically a torus. The map that takes each point in $\mathbb C$ to its corresponding point in ...
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1answer
46 views

Difference between “distribution” & “arrangement”.

Number of ways of Arrangement of $n$ different things into $r$ different groups is $$n!\binom{n - 1}{r - 1}$$. Number of ways of distribution of $n$ different things into $r$ different groups is the ...
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2answers
122 views

Use of either/or in maths

I have been using these two words for a long time, especially when representing the solutions to quadratic equations. But I am little confused. These terms are often used simultaneously, but it seems ...
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1answer
54 views

“Sharp” Inequalities

When we say that an inequality is sharp, does it mean that it is "the best" inequality we can get between the two quantities involved? For example, I read that we would say that the inequality $$ ...
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0answers
30 views

Notation: column/row projection function for matrix-like objects

If we have a $n$-tuple $\mathscr x$ $$\mathbf{x} := (x_i)_{i\in n}=(x_0,x_1,\ldots,x_{n-1})\in \prod_{i\in n}X_i$$ where $(X_i)_{i\in n}$ is an indexed family of sets and $x_i\in X_i$. We can ...
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0answers
95 views

Submodules $H$ satisfying: “if $ax \in H$ for some non-zero scalar $a$, then $x \in H$.”

Suppose $R$ is a commutative ring and that $X$ is an $R$-module. Question. Is there a term for those $R$-submodules $H$ of $X$ satisfying the following? For all $x \in X$, if $ax \in H$ ...
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0answers
22 views

Definition of a minimal set of automorphisms generating an orbit?

By definition, the orbit of a vertex v in a graph G is the set of all vertices f (v) such that f is an automorphism of G. I wonder whether there is a definition for a minimal set S of automorphisms ...
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2answers
22 views

Is there another terminology to designate this?

Let $R$ be a principal ideal domain. Let $M$ be a finitely generated $R$-module. Then there exists a free $R$-submodule $F$ of $M$ such that $M=Tor(M)\oplus F$ and the ranks of such $F$'s are the ...
6
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2answers
123 views

If $a=b$ then $a+c=b+c$? [duplicate]

A friend of mine just asked me how to prove that if $a=b$ then $a+c=b+c$, where $a,b$ and $c$ are real numbers, I'm not sure what I should answer. I have a book called introduction to logic and to the ...
6
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2answers
221 views

Why is $\sinh$ often pronounced “shine”?

I talked to some guys from the UK and they told me that they would pronounce $\sinh$ as "shine". I am not a native English speaker so I don't know, but in my country we call this function "sintsh" ...
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1answer
26 views

Are there terminologies distinguishing these two ranks?

Definition 1. Let $R$ be a ring with invariant basis number and $M$ be a free $R$-module. Then, the rank of $M$ is the cardinality of an $R$-basis of $M$. ${}$ Definition 2. ...
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1answer
23 views

Order of a polynomial in $\mathbb F_q[x]$

I came across the term "order" in the context of $\mathbb F_q[x]$, specifically of irreducible polynomials. Does this mean order in the group theoretical sense? I tried to prove that every polynomial ...
2
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1answer
85 views

Positive and negative logical connectives

By inspecting the rules of inference for (intuitionistic) predicate calculus (or, alternatively, thinking about double negation translation), one sees that there is a certain dichotomy between two ...
2
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1answer
75 views

Name of function $(1+x)^n-1$

Is there any name for this formula $$(1+x)^n-1$$ When working with floating point numbers this can be calculated with much better precision for very small $|x|<1$ values using Taylor series ...
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1answer
55 views

What is mutually disjoint sets

What is mutually disjoint sets? I know it has something to do with subsets but I don't know for sure.
4
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1answer
53 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 ...
2
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2answers
57 views

Why is it called the category of representations?

Let $A$ be a (Hopf) algebra. Let $C_A$ be a category whose objects are $A$-modules and whose morphisms are $A$-linear maps. This category is called "the category of representations". My question is: ...
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0answers
15 views

What is the nomenclature for the repeating part of a curve with n-repeating-peaks?

Below is a Google Trends search for "past papers", notice the curve has repeating portions where each repeat has three peaks at different levels. I want to know what the technical name of such a ...
3
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1answer
37 views

Convex functions up to reparametrization

I would like to know if there is a standard name for functions $f:[0,1]\to\mathbb R$ with the following convexity property: $$ \forall s<t<u\qquad f(t)\leq\max\{f(s),f(u)\}$$ (the fact that ...
0
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1answer
51 views

Lambert W-Function

Is there a standard name for the inverse of the Lambert W-Function, in the manner that the name "exponential function" is the name for the inverse function of the logarithmic function.
0
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0answers
37 views

Terminology for functions such that $f(x)\ge x$ for all $x$

Is there a common terminology for a real function $f$ such that $$f(x)\ge x$$ for all $x$? same question for the conditions $\forall x,f(x)>x$; $\forall x,f(x)\le x$; $\forall x,f(x)<x$. (I'm ...
3
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1answer
54 views

What does it mean for pullbacks to preserve monomorphisms?

If two arrows $f_A : A \to C$, $f_B : B \to C$ are monomorphisms, then their pullback arrows $p_A : P \to A$, $p_B : P \to B$ are monomorhisms too. Is that what is meant by pullbacks preserving ...
0
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1answer
29 views

How's this inertia called?

Let $E/F$ be an algebraic extension. Let $L_1,L_2$ be algebraically closed fields and $\sigma_1:F\rightarrow L_1,\sigma_2:F\rightarrow L_2$ be field monomorphisms. Define ...
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0answers
33 views

How is this commutator property $[a,b]=bx$ called?

If two elements $a,b$ commute like this $[a,b]=bx$ for some $x$ so that it can rewriten as $$ ba=a(b-x), $$ is there a term for such property? It is as if $a$ and $b$ almost commuted (but not quite) ...
1
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1answer
24 views

Mathematical Name for Physical Gauge Symmetries

In physics, when talking about a gauge transformation, we always mean two combined transformations. For example, a $U(1)$ gauge transformation is a combination of $$ \psi \rightarrow e^{ia(x)} \psi ...
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1answer
55 views

informal semantics regarding CH and AC

why is the assertion $\aleph_1=2^{\aleph_0}$ referred to as a hypothesis, whereas $$\forall \alpha( S_\alpha \ne \varnothing) \Rightarrow \prod_\alpha S_\alpha \ne \varnothing$$ is called an axiom? ...
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1answer
35 views

What are the names of these variations on the transpose of a matrix and symmetric matrices?

Is there a name for the operator that reflects a matrix over the diagonal running from the top-right to the bottom-left? For the moment, define this reflection of a matrix $A$ as $A^*$. Is there a ...
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0answers
20 views

Space of ternary codes

(Newbie question). Hamming space is the collection of all $2^N$ binary strings of length $N$. Is there a distinct name for the space of ternary codes? How about distinct names for the space ...
2
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3answers
78 views

What does inversion mean?

I am in highschool taking some advanced math courses and I have some questions about terminology. There appears to be more definitions to the meaning of inversion in math than I can count. I'm ...
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2answers
161 views

What is a “natural group action”?

Eg. The symmetric group on S acts on S in a natural way, for all sets S. Thanks in advance!
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1answer
56 views

Does the “equality semigroup” have an accepted name?

Given a set $G$, we get a semigroup on $G \cup \{0\}$ as follows: Define $x^2 = x$ for all $x \in G \cup \{0\}$. Define $xy = 0$ for all distinct $x,y \in G \cup \{0\}$. Question 0. Does this ...
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1answer
66 views

The name for predicting future rolls of dice based on the past

My friends and I were playing a game where you roll dice and you bet money on what picture it's going to land on and I began reasoning with myself that if I tallied up what pictures the dice landed on ...
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0answers
59 views

Name of the set $B:= \overline{A}\setminus A$

Let $(X, \mathcal{T}_X)$ denote a topological space and let $A$ be a subset of $X$. We define the set $B:=\overline{A}\setminus A$. Does the set $B$ have a special name in the literature? All I could ...
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0answers
19 views

Term for a graph with input and output ports

A Graph is a well-defined concept in mathematics, computer science and engineering disciplines that depend on them. However, oftentimes a practical implementation of a (directed) graph in a certain ...
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14answers
4k views

What does the term “undefined” actually mean?

I have read many articles on many sites and in many books to understand what undefined means? On some sites of Maths, I read that it could be any number. and on some sites, I read that it may be some ...