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

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0
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1answer
32 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
31 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
votes
1answer
38 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) ...
1
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1answer
20 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 ...
1
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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
36 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
145 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
51 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
23 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 ...
1
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0answers
57 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
32 views

A quadratic equation is expressed to zero, what is the less specific case of this called? [closed]

so we have an "expression" (no equals), we have an equation (has an equality), this is a type of equation because it is along the lines of x=0 or xy=0 I am looking for this word because it helps me ...
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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 ...
27
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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
50 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
votes
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 ...
1
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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 ...
1
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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 $y \to \infty$. ...
2
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2answers
33 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
145 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 = ...
0
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1answer
32 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
votes
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 ...
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0answers
102 views
+50

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 ...
1
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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
vote
3answers
76 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
votes
1answer
218 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 ...
1
vote
1answer
35 views

Term for relationship of set overlap without containment?

What is the term for the relationship between two sets that share at least one common element, but neither set is a proper or improper subset of the other? $$ A?B=_{def}\exists x \exists y \exists z ...
0
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0answers
11 views

Name of $\bar{F_E}$?

Let $E/F$ be a field extension. Define $\bar{F_E}:=\{\alpha\in E : \alpha \text{ is algebraic over } F\}$. What is the standard name of this? Fraleigh calls it 'the algebraic closure of $F$ in ...
9
votes
2answers
144 views

Is there a term for two polygons with the same angles but different side lengths?

Suppose polygons $A$ and $B$ have the same number of sides, and there is a correspondence between the vertices of $A$ and $B$, in consecutive order around both polygons, so that the angles at ...
1
vote
1answer
61 views

What is the difference between Boolean logic and propositional logic?

As far as I can see, they only employ different symbols but they operate in the same way. Am I missing something? I wanted to write "Boolean logic" in the tag box but a message came up saying that if ...
4
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0answers
74 views

In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

The Mean Value Theorem says approximately that for differentiable $f$, there is a $c \in (a,b)$ such that $$ f'(c) = \frac{f(b)-f(a)}{b - a}. $$ I presume that the number $f'(c)$ is the mean value. My ...
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0answers
27 views

Terminology: Opposite of “refinement”

Let A be a partition of a set, and B a refinement of A. Fill in the blanks: A is a __________ of B. I know that A is coarser than B, but how does one turn that into a noun?
2
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1answer
20 views

Is there a term for “mutually define”?

Today, I learnt about the relation between inner product space and normed space which parallelogram law holds. Then I had wondered about something like this: Let $A$, $B$ are 2 types of structures. ...
4
votes
1answer
40 views

What is the name for a rectangular figure of many sides?

What is a polygon where each edge is at a 90 degree or 270 degree angle to the prior edge (giving both concave and convex vertices) called? Here is one example of such a shape: ...
0
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2answers
27 views

Simple Explanation of Geometric distribution?

I really understood the explanation of Hypergeometric distribution by looking at this answer but when it comes to Geometric distribution I can't get how they calculate the probability distribution of ...
-1
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0answers
22 views

Weak compactness of the unit ball of $L^p$

What does it mean by weak compactness of the unit ball of $L^{\frac{m}{m-1}}$?
0
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1answer
23 views

More explicitly, what is $\left(p_n\right)_{n\in\mathbb{Z}}$ in this paper's context

I'm reading this paper and on page 3 between just prior to their mentioning of $\left(2\right)$ they state the following: ...if there is a sequence of polynomials ...
2
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0answers
24 views

Terminology for subsequences?

Note: I'll index all my sequences by $\mathbb N$, so I drop the indices in the sequence notation. The notion of a subsequence of a sequence $\{a_n\}$ is a sequence obtained by deleting some terms in ...
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0answers
16 views

“Branch” of a correspondence

I just saw for the first time references to the "branches" of a correspondence. Examples of the use of the terminology can be found in ...
3
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2answers
42 views

Function with an $x$ not in simple form

I've stumbled upon a practice example in an old textbook which I find confusing. Maybe it's because I haven't reached part of an explanation yet (went through pages, haven't found anything of help). ...
0
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0answers
12 views

Formally correct “generator expression” for parameters of a function

I'm trying to express formally correct that a class of functions exists that have a certain property that applies to all concrete "instances" of this class. In that I try to write a "generator ...
2
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0answers
27 views

Invariant subspace vs. irreducible subspace (terminology)

In a course in representation theory I was presented the following proposition: Let $(\pi,V)$ be a finite dimensional irreducible representation with a cyclic vector. $V$ has a unique max. proper ...