# Tagged Questions

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

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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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 ...
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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 ...
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### 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 $3^n$ ...
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### 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 ...
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### 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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### 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?
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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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.
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### 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 ...
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 ...