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

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1answer
83 views

Do function with the following property have special name?

I'm writing "a structure preserving surjection" way too much when I need to refer a function of the following property: $$ Y \subseteq Z, X \subseteq Z. g: Z \to A, g \text{ is some fixed function}.$...
0
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1answer
83 views

What is the meaning of “countable spread”?

I encountered an example that said: A Tychonoff 2-starcompact space of countable spread which is not $1\frac{1}{2}$-starcompact. My question is this: What's the meaning of "countable spread" ?
5
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7answers
1k views

Dictionaries and resources for translation of mathematical terminology

Nowadays English seems to be the most frequently used language in mathematics. (Although plenty of papers and books are published in other languages, e.g., Russian, French, German and Chinese.) ...
9
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3answers
247 views

Is there a name for a semigroup whose idempotents form a subsemigroup?

For a semigroup $S,$ I will denote by $E(S)$ the set of all idempotents of $S$. For $X\subseteq S,$ let $X^2$ mean $\{xy\,|\,x,y\in X\}.$ Is there a name for the class of semigroups $S$ such that $$\...
0
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1answer
510 views

Name for a graph with two types of vertices $U, V$, where the end points of edges are either both in $U$, or one is in $U$ and the other in $V$?

I know that a graph whose vertices can be divided into two sets $U$ and $V$ such that every edge can only connect a vertex in $U$ to one in $V$ is called a bipartite graph. Is there a name for a type ...
0
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1answer
189 views

Meaning of the term single letter formula

It is common in information theory to look for single letter formulas or to dismiss a result as suboptimal if no single letter formulas are available. Could someone clarify the meaning of what is a ...
0
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0answers
88 views

Is there a name for a subset $S$ of a group or a semigroup such that every two elements of $S$ commute?

Let $G$ be a group and $S$ its subset. I would like to consider the following condition on $S$. For every $x,y\in S,$ we have $xy=yx.$ This is trivially equivalent to $S\subseteq C(S).$ The ...
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1answer
86 views

whats the order of a distributional derivate?

I have to calculate the derivatives of order $\le 2$ of for example $f(x) = |x|$, is it the same as the second derivate, what does this "of order $\le 2$" mean? calculating distributionell derivatives ...
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0answers
34 views

Terminology: Subrings with the property that an element is invertible iff it is invertible in the larger ring. [duplicate]

Possible Duplicate: Is there a term for an “inverse-closed” subring of a ring? This is a question about terminology. Is there a standard name for a subring $A \subset B$ that has ...
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1answer
144 views

terminology of multilinear form

In the litterature we see the terminology "multilinear form" or "$n$-form". I'm used to refer the word "form" to mean a homogeneous polynomial. but here we define it as a map $f:V^n\to F$, ($V$ is an ...
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1answer
604 views

Tuple definition

Is it correct? $S=\{\langle t,h\rangle:t\in\{0,\Delta t,2\Delta t,\cdots,24\},h\in\{0,\Delta h,2\Delta h,\cdots,H\}\}$ I would like to say that $S$ is a 2-tuple. The first tuple can vary from $0$ to ...
2
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0answers
180 views

Property similar to subadditivity

A function is called subadditive such that $f(x+y)\le f(x)+f(y)$ holds for any $x$, $y$ in the domain of $f$. (Let us say that, for example, the domain is some subset of $\mathbb R$ closed under ...
0
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1answer
133 views

Combination of n sets that produces a set of n-tuple

Given n sets with 3 elements: $X_i=\{a_i,b_i,c_i\}$ where $\{i\in\mathbb{N}|1\leq i\leq n\}$. How can I define a n-tuple based on combination of this sets that produces the set $S$ with $3^n$ ...
2
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1answer
184 views

Probability distribution explanation

What exactly is a probability distribution, and what are the two requirements for a probability distribution? I am not sure what this means or how to apply it? Any examples that can be given would ...
22
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1answer
580 views

An interesting topological space with $4$ elements

There is an interesting topological space $X$ with just four elements $\eta,\eta',x,x'$ whose nontrivial open subsets are $\{\eta\},\{\eta'\},\{\eta,\eta'\}, \{\eta,x,\eta'\}, \{\eta,x',\eta'\}$. This ...
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1answer
2k views

Name of proof that area of square>area of rectangle of the same perimeter

What is the proof called for the fact that the area of a square is always greater than the area of a non-square rectangle of the same perimeter?
2
votes
1answer
64 views

Vector as argument of a function

Given a function $f(x)=y$ is correct to say that $f\left(\left[\begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array}\right]\right)=\left[\begin{array}{c} y_1 \\ y_2 \\ y_3 \end{array}\right]$?
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2answers
853 views

What is the thing inside a sum called?

You know how the "thing" inside an integral, we call that an integrand. Does any know what the $a_n$ in a typical $\sum a_n$ is called? Or do we only have names if it is an infinite series? I could've ...
4
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2answers
180 views

What consitutes an exponential function?

I was recently having a discussion with someone, and we found that we could not agree on what an exponential function is, and thus we could not agree on what exponential growth is. Wikipedia claims ...
6
votes
1answer
155 views

An “independence” condition on two algebraic elements over $K$.

Let $K$ be a field and let $a,b\in \overline K$ be algebraic elements. I've stumbled upon a certain condition on $a,b$, which I feel could be considered an "independence" condition. I would like to ...
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1answer
5k views

Quantile and percentile terminology

Note: This is answered by user974514 below, but there was some discussion outside of the "answer", so I paraphrased the final answers inline here. I've asked around for the exact usages of the terms "...
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1answer
222 views

What does “+ complete” mean?

I'm reading notes about Liapunov stability, and in the book of Abraham, Marsden and Ratiu I found the next definition: Let $m$ be a critical point of $X$. Then $m$ is stable (or Liapunov ...
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1answer
23k views

Numerator vs. denominator vs. nominator

What is appropriate usage of "numerator", "denominator", and "nominator" to refer to parts of a fraction? I'm posting this question and answer here because I had little luck finding a clear answer ...
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2answers
615 views

Number of elements vs cardinality vs size

I have been wondered the definition of cardinality and number of elements. One mathematician told me that one can't said that the cardinality or size of the set $\{1\}$ is one, it should be said that ...
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1answer
121 views

Is there a name for this ideal constructed in terms of two submodules?

If $M$ is an $R$-module and $M_1, M_2$ are submodules of $M$, then one can construct the ideal $\{ r \in R \mid rM_2 \subseteq M_1 \}$, which is denoted $(M_1 : M_2)$. Does this construction have a ...
2
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1answer
88 views

Is there a word to describe the set of permutations of each member of the powerset of a set?

Just what it says on the tin: For a set, X, is there a word to describe the union of sets of permutations of each member of the powerset of X?
2
votes
1answer
75 views

Terminology for a function computed by a finite-state transducer?

A finite-state transducer is a generalization of a finite state machine that accepts an input string and produces an output string (instead of just accepting or rejecting). Is there a name for a ...
14
votes
4answers
671 views

Why the terminology “monoid”?

As I am not a native English speaker, I sometimes am bothered a little with the word "monoid", which is by definition a semigroup with identity. But why this terminology? I searched some ...
0
votes
1answer
300 views

What does face-width mean?

What is the meaning of the term face-width? I have seen the term used as a property of an embedding of a graph on a surface. I haven't found a definition.
2
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0answers
49 views

Is there a name for the number of edges that need to be removed to lower the genus of a graph?

The number of edges that need to be removed from a graph to disconnect it is called the edge-connectivity. Similarly, given a graph of genus $n>0$, there is a minimum number of edges that you have ...
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1answer
498 views

Generalization of the matrix concept

It has been some time since I left university... In a not too formal language, an $n$-dimensional vector is an indexed set of numbers $\{i_1, ..., i_n\}$. A $n\times m$ matrix is a set of numbers ...
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2answers
3k views

What is the difference between the terms “classical solutions” and “smooth solutions” in the PDE theory?

What is the difference between the terms "classical solutions" and "smooth solutions" in the PDE theory? Especially,the difference for the evolution equations? If a solution is in $C^k(0,T;H^m(\Omega))...
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votes
4answers
436 views

What does it mean to take the splitting field of $f(x)\in F[x]$ over $K$ where $K/F$ is a field extension

Let $K/F$ be a field extension and let $f(x)\in F[x]$. I know $f(x)$ have a splitting field, i.e. a field $E$ that $f(x)$ splits in ($E/F$ and $f(x)$ doesn't split in any proper subfield of $E$). I ...
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0answers
70 views

Is there a standard name or shorthand for “plustorial”? [duplicate]

Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? We're all familiar with factorial: $$n>0,\quad n! = n \times (n-1) \times \...
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1answer
97 views

Whether to use 'OR' or 'AND'

My doubt is: while solving equations or inequalities consisting of absolute values when should we use the conjunction 'OR' and when to use 'AND'? whats the difference between them ?
0
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1answer
836 views

Am I abusing the word “remark”?

My professor often uses the word "remark" to comment on something. I find myself picking it up and also replacing that word for "comment" Does it look silly to do that? Or is the word "remark" can be ...
4
votes
2answers
165 views

A formal name for “smallest” and “largest” partition

Consider a set $A=\{1,2,3,4,5\}$, is there any terminology for the following partitions of $A$ ? (1) $A=\{ \{1\},\{2\},\{3\},\{4\},\{5\} \}$ (2) $A=\{\{1,2,3,4,5\}\}$.
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2answers
520 views

What are the carried numbers called in an Addition problem

What is the 1 that is carried called? These are all Latin, would this make sense? The Latin word for "carry" is "porto", would it be called Porto? Just guessing here Example: ...
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1answer
1k views

Continuous and Open maps

I was reading through Munkres' Topology and in the section on Continuous Functions, these three statements came up: If a function is continuous, open, and bijective, it is a homeomorphism. If a ...
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2answers
1k views

Why is the topological pressure called pressure?

Let us consider a compact topological space $X$, and a continuous function $f$ acting on $X$. One of the most important quantities related to such a topological dynamical system is the entropy. For ...
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1answer
295 views

Parameter or independent variable?

I need an explanation of the difference between parameter and variable in the following example. In extremal geometric problems when we want to find the object having some extremal property, say ...
88
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6answers
3k views

Why does mathematical convention deal so ineptly with multisets?

Many statements of mathematics are phrased most naturally in terms of multisets. For example: Every positive integer can be uniquely expressed as the product of a multiset of primes. But this ...
6
votes
1answer
289 views

What are “Lazard” sheaves?

Early in Categories, Allegories, by Freyd and Scedrov (p.12, in the section on basic examples) there appears the following example: Let $\mathcal{LH}$ be the category whose objects are topological ...
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2answers
749 views

Usage of the word “formal(ly)”

This is weird. To me, in mathematical contexts, "formally" means something like "rigorously", i.e. the opposite of informally/heuristically. And yet, I very often read papers very the word seems to ...
0
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1answer
92 views

“fluent” functions

In an old mathematics book (Ritt, 1948, p.5) I have come across the notion of "monogenic analytic" and "fluent" functions. These are complex valued functions. Has anyone heard of these terms before? I'...
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votes
1answer
2k views

What is the meaning of evaluating the divergence at a _point_?

Reading this first, Divergence (div) is “flux density”—the amount of flux entering or leaving a point. Think of it as the rate of flux expansion (positive divergence) or flux contraction (negative ...
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0answers
172 views

How to read equations and expressions out loud? [duplicate]

Possible Duplicate: Is there a definitive guide to speaking mathematics? This may be an incredibly stupid question, but I was wondering how would one pronounce simple mathematical equations ...
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1answer
92 views

Graph of a Rel-morphism

Let $F=(f;A;B)$ is a morphism of the category $\mathbf{Rel}$ (the category whose objects are sets and morphisms are defined as binary relations). How to name and how to denote $f$ when we know $F$? ...
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0answers
1k views

What does normalization in math mean.

I have encountered something like this in a paper and was wondering what it really means normalize the local values in a manner that it leads to elegant probalistic interpretation Its not that ...
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1answer
90 views

Name this property: First symmetric group in which a given group appears

For all finite groups $G$, define $S(G)$ to be the smallest $n\in\mathbb{Z}^+$ such that there exists an $H\leq S_n$ isomorphic to $G$ — i.e., $S(G)$ is the index of the first symmetric group in which ...