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

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0answers
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Inverses of two argument functions with respect to one argument

Consider a function $f : A \times B \to C$ and two inverses, each with respect to one argument; i.e. $g$ and $h$ defined such that $f(x,y)=z \iff g(y,z)=x \iff h(z,x)=y$. A simple example is addition: ...
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0answers
59 views

Functor whose values on morphisms are monomorphisms

Is there a name for a functor whose values on morphisms are monomorphisms?
4
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3answers
173 views

When does something become a “mathematical object”?

A mathematical object is an abstract object arising in philosophy of mathematics and mathematics. Abstract object: Abstract and concrete are classifications that denote whether a term ...
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1answer
106 views

Formal Mathematical Terminology For Tree Diagrams

I currently have a tree diagram that shows the probabilities for certain paths in a game. The tree diagram first branches into four possibilities and then another four possibilities for each of the ...
2
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2answers
35 views

Is there an object which groups two vectors together?

Is there a single name for a pair of vectors that together describe a position and orientation? Like an "oriented point" or something like that?
5
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2answers
794 views

Is 9/1 an improper fraction?

My son took a test in school. The teacher told them that they did not need to simplify improper fractions in their answers. On one question, for example, the answer of 28/3 was marked as correct. ...
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0answers
56 views

Teminology: Partitioning a Set Including Empty Partitions

Mostly I see a partition of a set A defined as a collection of non-empty disjoint sets whose union is A. I see one reference that allows empty sets to be included in the partition: ("Potter, M. "Set ...
2
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1answer
48 views

terminology of differences

When quantity a changes to b, it can be said that the difference is d = b - a. I might call ...
2
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0answers
32 views

Soft question on “what” vs “which” when referring to sets of numbers [closed]

Maybe this question is completely inappropriate for this forum. I therefore apologize in advance and welcome anyone to close it should this be the case. When referring to elements of sets, should you ...
1
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0answers
52 views

Is This Still Chain Homotopy?

Two maps between chain complexes are homotopic if there is a function $P$ such that $$ f-g=\partial P+P\partial. $$ What if we instead had $$ f-g=\partial P? $$ Then $f$ and $g$ still induce the same ...
4
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3answers
111 views

What is meant by 'runs through'?

I'm independently studying abstract algebra for fun (not my forte...) and I'm reading Herstein. He has a question in the chapter on rings: Let $p$ be an odd prime and ...
2
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3answers
72 views

What does “nilpotent” in a “nilpotent group” mean?

It seems to have nothing to do with the usual nilpotency, i.e. $\exists n\in \mathbb{N}:x^n=0$. Actually I think the latter only makes sense in a ring or more rich structure. I tried to relate some ...
3
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1answer
60 views

Is there a name for the value $x$ such that $f(x)$ is maximum?

Obviously, $f(x)$ is called the "maximum value" or simply "maximum", but what is $x$ called? The maximizer? Additionally, what if $f(x)$ is minimum or simply an extremum?
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1answer
155 views

Given two overlapping datasets (think Venn Diagram), what is the point/plane called that separates the middle from either side?

Or, if you prefer a typed out version: Given the following two datasets: [Category A]: 1,3,4,7,8,9,13 ... 28,30 [Category B]: 29,32,33,37 ... 61,62,63 Plotted ...
0
votes
1answer
138 views

How to describe a “sum percentile”

I have values $w_1 \ge w_2 \ge ..\ge w_n$. I want to know the the highest possible threshold $w^{th}$ so that $$ \sum_{i:w_i>w^{th}} w_i \ge \alpha \sum_{i=1}^n w_i $$ where $\alpha \in [0,1]$. ...
4
votes
1answer
95 views

Why do we traditionally use letter U for open sets?

Most of traditional usages of symbols in mathematics have origin in English, German or French words that start with that letter, for an example: $p$ for a prime number, $\mathbb{Z}$ for integers (ger. ...
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4answers
91 views

What is the difference between the terms 'equation' and 'algorithm'?

What is the difference between the terms 'equation' and 'algorithm'? Can these terms be used interchangeably?
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5answers
253 views

Reflexivity: How can something be related to itself?

Background: I'm a philosophy student. I'm comfortable with math, but don't have much of a background in it. One of the topics I'm writing about (I-relation in theories of identity) closely mirrors ...
1
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2answers
107 views

Partial functions - where can I learn more about this (heuristic, informal) system of conventions?

Is there a name for the following (heuristic, informal) system of conventions for dealing with partial functions and undefined expressions? I'd like to know whether it has any undesirable quirks that ...
3
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1answer
120 views

Why “Syracuse” in “Syracuse problem”

Is “Syracuse” in “Syracuse problem” (a variant name of Collatz conjecture) a reference to the city of Syracuse in Sicily, to one of several Syracuses in USA or something else (a person's name, for ...
1
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1answer
32 views

Matrices as Functions

A friend of mine was criticized in undergrad by a Professor for saying that a matrix is a function. Now, a matrix can be represented by a linear transformation, and linear transformations by ...
2
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3answers
3k views

In graph theory, what is the difference between a “trail” and a “path”?

I'm reading Combinatorics and Graph Theory, 2nd Ed., and am beginning to think the terms used in the book might be outdated. Check out the following passage: If the vertices in a walk are ...
3
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1answer
83 views

Completing a Partially Defined Associative Binary Operation

This is more like a question about terminology. I would like to hear some recommendations of books that discuss algebraic structures with one partially defined associative binary operation, and the ...
5
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0answers
132 views

Why are they called orbits?

When we study actions in group theory, we consider sets of the form $$\text{Orb}_G(x)=\{gx\mid g\in G\} $$ that are called orbits. Although, the only reason I find convincing for that name is that in ...
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1answer
56 views

Whats the name of this function?

I read this function in an exercise. It looks quit familiar to me, however I do not know its name. Whats the name of the $\rho_n$ function and who brought it up first?
-1
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1answer
116 views

Sum-to-one constraint

This is a general question, but I am asking it since I am not able to find any good material online. Can someone please explain what's meant by a "sum-to-one constraint"? Thanks.
4
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1answer
83 views

On group theory terminology

Let $G$ be a finite group. Consider the next number $$m(G):=\min\{m\in\mathbb{N}\mid G\ \text{can be embedded into}\ S_{m}\}.$$ It is obvious that Cayley's theorem yields $m(G)\leq |G|$. My ...
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2answers
88 views

Coupled nonlinear PDE, how to find solution, is this a well-known problem?

During my weekly meeting with a student we stumbled upon a curious system of PDEs. Here $u,v$ are functions of $x,y$ and $$ \frac{\partial u}{\partial x} = u^2+v^2 \qquad \frac{\partial v}{\partial ...
2
votes
2answers
970 views

What is the statement “If not p then q” called?

Let's say I have a statement: if p then q. The converse would be: if q then p. The inverse would be: if not p then not q. The contraposition would be: if not q then not p. What would you call the ...
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0answers
21 views

Terminology for a graph that can be drawn in several planes?

A graph is called planar if you can draw it in the plane without any edges crossing. In circuit layouts, it's common to try to lay out a graph across multiple different planes, where edges can jump ...
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1answer
71 views

What is a cycle hypergraph?

What is a cycle hypergraph? Could someone give me good reference or illustrate with a few examples?
0
votes
1answer
22 views

Descriptive statistics, percentage of values in interval

I have a list of values representing estimation errors, like { 1, 3, 7, 16, 5, 4, 3, 1 }. Now I determine the percentage of estimations below/equal a specified ...
1
vote
0answers
74 views

Graph theory name for minimum depth to leaf node.

In a graph theory rooted tree, is there a name for the minimum depth downwards to reach a leaf node? I have in mind calculating "depth to a leaf" at each node by looking downwards through the subtree ...
7
votes
1answer
297 views

What is “observation”?

Often in mathematical writing one encounters texts like ''..we observe that this-and-that..''. Also one may find a review report basically saying ''..the paper is just a chain of observations...''. ...
2
votes
1answer
226 views

Sum of Two Convex Sets

A friend of mine recently got an assignment, which asked for the sum of two convex sets in $\mathbb{R}^n$. Is this sum referring to Minkowski addition or is there another meaning to it? (such as the ...
2
votes
2answers
130 views

The use of any as opposed to every.

This is a really basic question, but it is one I never really thought about until now. Let $\mathscr{G}$ be a tree. Then every pair of vertices in $\mathscr{G}$ is connected by a unique walk. We ...
3
votes
1answer
46 views

Minimality in the case of partial derivatives and Sobolev spaces?

I am trying to understand this question here that considers Sobolev spaces apparently and hence partial derivatives. What is the definition of minimality there? Is the minimality defined by ...
0
votes
1answer
56 views

Find minimal $\alpha_3$ such that $u\in H^3(\Omega)$ and $u(x,y,z)=x^\alpha(1-x)y(1-y)z(1-z)$

My instructor presented me the quiz below but forgot to define key terms such as minimality and $H^3$. Quiz Let $u(x,y,z)=x^\alpha(1-x)y(1-y)z(1-z)$. Find the minimal $\alpha_3$ such that $u\in ...
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2answers
397 views

Is there a name for functions that are their own inverses

There are terms for various kinds of functions (or operators) such as... ...
0
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1answer
1k views

Minimal Spanning Set vs Basis of a vector space

I read the following in my textbook: Find as small a set of vectors that span the row space of $A$ as you can. Such a set is called a minimal spanning set. Is this terminology synonymous with ...
1
vote
1answer
102 views

Is there a way to mathematically describe “surprise”?

Let's say that there are ten people entered into a random drawing, the winner gets some large prize. If I were one of those ten people, and I were to win, then I would be pleasantly surprised. If ...
0
votes
1answer
66 views

What do we call the state of being proper?

The set $\{1, 2\}$ is a proper subset of $\{1, 2, 3\}$. But $\{1, 2, 3\}$ itself is not. More generally, we might want to define a notion of "proper-ness" that derives from this basic notion of ...
9
votes
1answer
512 views

On a joke of Yoneda embedding

I have heard a joke like this: The Yoda embedding, contravariant it is. And a joke concerning "How to put an elephant into a refrigerator", a comment from "Category Theorist" says Isn’t this ...
1
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1answer
353 views

What is a tail sequence?

The question is self-explanatory. What is a tail sequence or a tail of convergent sequence? Thanks
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0answers
36 views

Is there a word that means “theorem (in context), possibly with free variables”?

Suppose I write down some assumptions... $a < b$ $b < c$ ...and deduce some stuff... $a < c$ $a \neq c$ is there a word that covers both my assumptions, and the things I've deduced? For ...
2
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1answer
56 views

“Set” vs “collection” terminology: what is the difference?

Can someone tell me what is the difference in saying $A$ is a set of even numbers and $X$ is a collection of even numbers ?
6
votes
4answers
125 views

The limit of $f$ or the limit of $f(x)$?

I have read before that $f$ denotes the function $f$ whilst $f(x)$ denotes the value of the function $f$ at $x$. What is right? To say that the limit of $f$ as $x$ tends to $a$ is $L$ or to say that ...
2
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1answer
37 views

What is the term for a relation whose inverse relation is serial?

A relation $R$ is serial iff $\forall x, \exists y, xRy$. What is the name of the inverse property stating that $\forall y, \exists x, xRy$? And is there a name for the property which is the ...
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0answers
36 views

Is there a special name for matrices with $M[j,i] = M[i,i] - k, i \neq j$?

Backgroud: I am working on a computer science problem and arrives at a matrix $M$ with the following property: The size of Matrix $M$ is $n\times n$. For each row $j$, we have $M[j,i] = ...
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2answers
51 views

Graphs with pairs of vertices connected by multiple edges

Is there a common name for this kind of graphs (directed or not)? Thank you.