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

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1answer
42 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 ...
1
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1answer
36 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
15 views

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

If we have a $n$-tuple $\mathscr x$ $$\mathscr x := (x_i)_{i\in n}=(x_0,x_1,\ldots,x_{n-1})\in \prod_{i\in n}X_i$$ where $(X_i)_{i\in n}$ is an indexed family of sets and $x_i\in X_i$. We can ...
0
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0answers
28 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
16 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
20 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
115 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 ...
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2answers
174 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" ...
0
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1answer
25 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. ...
3
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1answer
16 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 ...
1
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1answer
32 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
70 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 ...
-3
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1answer
26 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.
3
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1answer
28 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
54 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
8 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
32 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
42 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
32 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
43 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
27 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 ...
2
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0answers
30 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) ...
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1answer
21 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
52 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? ...
0
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1answer
34 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 ...
0
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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 ...
3
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3answers
38 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 ...
4
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2answers
146 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!
4
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1answer
52 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 ...
0
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1answer
25 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
58 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
18 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 ...
28
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15answers
3k 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 ...
0
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1answer
33 views

Do the values above and below a Sigma in a summation have a name?

As the title asks: do the numbers above and below a sigma have a specific technical name? I am trying to describe an inefficiency in an algorithm, where the set of items used in the summation could ...
2
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0answers
51 views

What do we call $\mathfrak{M}$?

I am starting to learn some measure theory, and I was wondering if there is a name for $\mathfrak{M}$. I have the definition: A collection $\mathfrak M$ of subsets of a set $X$ is said to be a ...
0
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1answer
16 views

Terminology for when a variable is implicitly a member of some set?

I have sets $N = \{1, \ldots, n\}$ and $M = \{1, \ldots, m\}$. When referring to a generic element of these sets, I typically use variables $i \in N$ and $j \in M$. Is there any standard ...
4
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2answers
426 views

English for “prolongement” oder “Fortsetzung”?

I'm sorry if that's not the right place to ask for, wikipedia failed to give me the correct word... What's the english for a function that is defined on a larger domain than the original function and ...
1
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1answer
40 views

Is there accepted name for digraph segement without “joins” or “turns”?

As example lets consider following directed graph: ...
0
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2answers
46 views

What's the name of this wavy curve?

What's the name of the curve you get from changing the x or y frequency on what was previously a path around an ellipse? The equation would be: f(t) = (Acos(ut), Bsin(vt)) And it looks like a wavy ...
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1answer
46 views

How is this particular arithmetic expression called?

A normal arithmetic expression looks like this, right?: 3 + 5 * 3 + 14 / 7 The same expression written in Scheme looks like this: ...
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4answers
1k views

Is there anything special about this matrix?

I've just encountered a matrix which seems to display nothing special to me: $$B=\begin{pmatrix}1&4&2\\0 &-3 &-2\\ 0 &4 &3 \end{pmatrix}$$ But further observation reveals ...
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0answers
30 views

Does this PDE have a name? $y u_{xx} + u_{yy} = 0$

I am asked to solve the following equation: $$y u_{xx} + u_{yy} = 0, \quad -\infty < x < \infty, \quad y > 0, $$ together with $u(x,0) = \cos{qx}$ and bounded solution when $y \to \infty$. ...
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2answers
34 views

Linear algebra terminology: unique, trivial, non-trivial, inconsistent and consistent

Let me get this straight: Unique solution- has an exact solution (such as a POI of 2 intersecting lines) Trivial solution- when 0 needs to equal the zero vector in $Ax=0 vector$ Non-Trivial-? ...
2
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2answers
146 views

Why did they need to say that the image is a subset?

I'm reading the course notes on rings at the moment, but noticed something that didn't quite make sense immediately to me. Suppose $R$ is a ring and $f : R \to S$ is a homomorphism. Let $T = ...
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1answer
33 views

Is this alternate definition of Limit correct?

Would it be correct to define the limit of a series as the smallest number that no number in the series is greater than (for an increasing series, the other way around for a decreasing series, i.e the ...
0
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1answer
37 views

change the order of the digits of a prime number

What is prime numbers called, that if you arbitrary change the order of its digits, you will only get another prime number. For example 79 (79 is prime number as well 97) or 199 (199, 919, 991 is ...
4
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1answer
144 views

What is the difference between Calculus and Analysis? In Stochastic processes?

I guess one could say that Calculus is just a non-rigorous version of Analysis. What about in subjects involving stochastic processes? I took up masteral classes called stochastic calculus. I plan to ...
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1answer
33 views

Modifying the Peano Axioms to allow multiple successors

If you took the familiar Peano Axioms and replaced the axiom $x \in \mathbb{N} \implies \exists y\in \mathbb{N}(y =S(x))$ with $x \in \mathbb{M} \implies (\exists y_1\in \mathbb{M})(\exists ...
1
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3answers
77 views

What is the name of a number ending with zero's?

I am currently writing a very specific graph of a function implementation. The graph can have min/max values e.g. $134$ and $1876$ respectively. I'm calculating "nice" numbers. For min/max they are ...
5
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1answer
220 views

What does “hom” stand for in hom-sets and hom-functors?

With given category $\mathcal{C}$ and its objects $A$ and $B$, a hom-set $\hom_\mathcal{C}(A, B)$ is the collection of all morphisms from $A$ to $B$. There is also a related notion of hom-functor ...