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

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2
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1answer
656 views

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it? Thanks.
0
votes
1answer
21 views

Is the interior of a simple polygon, simply-connected?

This may be trivial, but I want to be sure I understand correctly: Is it true that the interior of a simple polygon is always a simply-connected subset of the plane? I.e, is it eligible for the ...
1
vote
0answers
16 views

Term for maximal proper divisors

What do you call a divisor, $d$, of a number $n$ which is of the form $d = n/p$ where $p$ is a prime divisor of $n$? For a cryptography class I need to discuss such numbers (to describe how to find ...
0
votes
0answers
32 views

Standard name or notation for the “even part” of an integer?

\begin{align} 0 & \mapsto 0 \\ 1 & \mapsto 0 \\[6pt] 2 & \mapsto 2 \\ 3 & \mapsto 2 \\[6pt] 4 & \mapsto 4 \\ 5 & \mapsto 4 \\[6pt] 6 & \mapsto 6 \\ 7 & \mapsto 6 \\ ...
58
votes
5answers
7k views
1
vote
1answer
22 views

What does it mean a transitive permutation?

let $X$ be a finite set. Let G be a group. What is the meaning of $G$ is a transitive permutation on set $X$?
0
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0answers
14 views

Approximate ratio with a small fraction so that numerator multiplied by denominator give enough rectangular area?

I would like to layout given number of objects (like plots) into rectangular area (like computer operating system window on screen). I would like to calculate the width and height of the window (in ...
0
votes
1answer
19 views

4 parameter logistic Law

It is well known that the four parameter logistic law has the following form $$ F(x)=D+\frac{A-D}{1+\Big(\frac{x}{C}\Big)^B} $$ What characterise this curve is its four parameters. A=starting ...
-1
votes
2answers
99 views

What does it mean to say “again” or “finally” in math? [on hold]

According to math rules if we say again, does it mean we are saying repeat previous step? For example: You have $10$ coins. Add $10$ more coins. Add $2$ coins Again $2$. Again $2$. Add $2$. And ...
1
vote
2answers
44 views

What exactly is the maximal solution of an ODE and why do we care?

I am reading these notes on the definition of a maximal solution of an ODE i.e. http://www.math.lmu.de/~philip/publications/lectureNotes/ODE.pdf But the definition is so abstract and no example is ...
0
votes
0answers
50 views

What kind of algebraic structure is $\left( \mathbb{R}_{\geq 0},+,\cdot \right)$?

Let $\left( \mathbb{R}_{\geq 0},+,\cdot \right)$ denote the non-negative real numbers with usual addition and usual multiplication. Obviously, this is not a field, because $0$ is the only additively ...
0
votes
0answers
43 views

Definition of fixed point free relation

If we have such relation that for $\forall x$ $f(x)\ne x$ , how is it called in one word? I can come up with only "graph of this function is not a straight line:)" Thank you
1
vote
1answer
39 views

Name of and references for the equivalence relation $x \sim y :\Longleftrightarrow x^2 = y^2$

Playing around with the concepts of negativity and positivity, I came across the following equivalence relation defined for all elements $x,y$ of a field $\mathbb{F}$: $$ x \sim y :\Longleftrightarrow ...
3
votes
1answer
36 views

Completing the square (and variants thereof)

When dealing with quadratics, completing the square is ubiquitous, and I can summarise my interpretation of it as the formula: $$x^2-2ax=(x-a)^2-a^2$$ Likewise, when working with circles (and, more ...
1
vote
1answer
19 views

Should an interpolation coincide the original function on the given data points?

Suppose having a model $f(x)=y$ where $f$ is unkown. Moreover, suppose you have some data points for this model i.e. $(x_1,y_1), (x_2,y_2), \dots , (x_n,y_n)$. If one can find an approximate of $f $ ...
5
votes
0answers
47 views

Is there a term for a function where equal output values must come from only one contiguous range of input values?

I'm looking for a word to describe a function where every output is guaranteed to have come from exactly one contiguous range of input values. For example, a monotonic function has this property, but ...
2
votes
2answers
37 views

What is the property of addition called when you break 97 into 100 - 3?

Sometimes it's easier to add numbers when you recognise that they're close to some round number, and then add the differences separately. $$97+198$$ $$=(100-3)+(200-2)$$ $$=(100+200)+(-3-2)$$ ...
1
vote
1answer
18 views

What is the name for the point where a non-smooth transition occurs

In the question Smooth transition between two lines (2d) there is an example of a composite curve which has a point where it is non-smooth. In general, what is the name for that transition point?
0
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0answers
46 views

Is there a name for the two parts of a complex number?

A complex number is the sum of a real number and an imaginary number. Is there a collective name for the two parts comprising a complex number, such that when used, it is (pretty) clear that the ...
2
votes
1answer
23 views

Is there a name for dividing a set into pieces, some of which may be empty?

Suppose that $X$ is a set and $V_{0}$, $J$, and $V_{1}$ are pairwise disjoint subsets of $X$ whose union is $X$. If the three subsets were nonempty it would be a partition of $X$. However, I wish to ...
43
votes
10answers
6k views

Is $0$ a natural number?

Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was considered in ...
3
votes
0answers
83 views

Name for categories with a certain property on coproducts

Is there a name for categories with the following property: The category has zero morphisms, coproducts, and for each family $(X_i)_{i \in I}$ of objects the natural map $$\hom(Y,\bigoplus_{i \in I} ...
2
votes
1answer
51 views

Seeking more information regarding the “hybriation function.”

Definition 0. Given a pair of finite sets $Y$ and $X$, write $Y_X$ for the set of all collections $\mathcal{K}$ of functions $f : Y \leftarrow X$ that are closed under "hybridization", by which I ...
0
votes
0answers
21 views

Term for a “Cartesian union/intersection/difference” of set families

Let $A,B$ be two families of sets. What is a term for the following families: $$C = \{a\cup b|a\in A, b\in B\}$$ $$D = \{a\cap b|a\in A, b\in B\}$$ $$E = \{a\setminus b|a\in A, b\in B\}$$ Since ...
5
votes
2answers
6k views

What is the difference between an axiom and a postulate?

I hear about axioms in set theory and postulates in geometry, but they seem like the same thing. Do they mean the same thing but then are used in different instances or what? Is one word more ...
1
vote
1answer
31 views

“vector” vs “point” in definition of directional derivative

Given a function $f\colon \mathbb R^n\to\mathbb R$, and given $x,v\in\mathbb R^n$, it is customary to define the "directional derivative of $f$ in the direction $v$ at the point $x$" by $$ D_v f(x) = ...
2
votes
1answer
28 views

$n$th root of $x$ - technical term for $n$?

As you can see in the title, I want to know how the number before a root is called. For example, if you have the cubic root of 8, I want to know how the 3 before the roof is called. Actually, I ...
0
votes
2answers
31 views

“conjugate to/with” or “conjugated to/with”, a terminology question in group theory.

This is a terminology question from a non-native English speaker. Let $G$ be a group and $a,b\in G$ such that there exists $c\in G$ verifying : $$b=cac^{-1} $$ I could say : the element $a$ is ...
0
votes
2answers
32 views

What is the connection between $l_p$ norms and “$l_p$ metrics”?

In some textbooks metric spaces you sometimes encounter these "$l_p$ metrics", $d_1, d_2, d_\infty$ (I don't think $l_p$ metric is very standard usage) For example, $d_1(x,y) := \sum\limits_i^m ...
34
votes
9answers
2k views

Definition of “well defined” in mathematics

I have encountered this term "well defined" in many places in maths like well-defined set, well-defined function, well-defined group, etc. What are the contexts in which we can talk about well ...
3
votes
1answer
53 views

Is there a name for subtracting a set of values from their max?

I hope this question is appropriate here - if it isn't let me know and I will remove it. I am wondering if there is a verb for the following operation: given a set of non-negative numbers, I take ...
1
vote
2answers
71 views

What's the name for the property for which $x + x = 0 \Longleftrightarrow x = 0$?

I have a set $\mathbb{S}$ for which I have defined an operation: addition ($+ : \mathbb{S} \times \mathbb{S} \rightarrow \mathbb{S}$). The structure $(\mathbb{S}, +)$ is a group. I have shown that if ...
2
votes
1answer
69 views

Less suggestive terms for “vector addition” and “scalar multiplication”

Question Are there less suggestive terms for the two operations commonly referred to as vector addition and scalar multiplication? Background In linear algebra, we use the terms vector addition and ...
0
votes
0answers
48 views

Is there any difference between “for any” and “for all”?

When we prove something, we use mathematical symbol ∀ to stand for "for all." Does it make any difference if we use same symbol for "for any."?
2
votes
1answer
51 views

Set of the vertex sets to make connected graph into disjoint sets of vertices?

Suppose a non-directed graph G with vertices V and paths P. What is the name for the vertex sets to make break the graph by removal of some vertices?
0
votes
1answer
21 views

Understanding a terminology in a special type of group

I am trying to understand the following terminologies, and the resulting group (found in this link). In the original reference also, I didn't find the meaning of the terminology I am looking. It is ...
0
votes
1answer
25 views

Part of a sigmoid function?

I revised a sigmoid function to use in my research. The function looks like this. $$ f(x) = 0.4 \cdot \frac{1}{1 + e^{-5x}}+ 0.3 $$ where $ x \in [-1,1] $. Is there a specific name to refer to this ...
7
votes
3answers
151 views

G/N read as G modulo N.

In my abstract algebra course, the instructor is calling G/N (the set of left Cosets of N in G) G mod N. This has not yet been explained. Why is this the case? My immediate suspicion is some ...
1
vote
2answers
27 views

Finding the probability space of the given experiment.

Specify the probability space completely for the following experiment: tossing a fair coin till we see the first heads. Here is what I have done so far: The sample space is simply $T^n H$ where $n$ ...
0
votes
0answers
20 views

Name of a number that matches place in a list?

I'm pretty sure there is a term for a number that has a value that matches its place in a list but my googling is failing me. For example in 4 2 2 4 1 0 the second 4 would have a special name.
1
vote
1answer
24 views

What does “modulo equivalence relationship” mean?

I am reading something on completion of metric spaces and it says: Let $\hat S$ be $\mathcal{C}$ modulo equivalence relationship of co-Cauchy sequences. Where $\mathcal{C}$ is the set is all ...
1
vote
0answers
28 views

Definition of mathematical expression

According to wikipedia: "In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical ...
0
votes
0answers
25 views

Are there clear, formal definitions for “terms” in subtraction operation?

I tutor children of all ages in Mathematics and I've noticed so many different words thrown around regarding binary operations, particularly with subtraction. For example, when working with a 2nd ...
7
votes
3answers
10k 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 ...
0
votes
0answers
25 views

Mathematics Terminology

I was reading a paper, and the paper stated: $Cov_t (\epsilon_{a,t+1}, \epsilon_{b,t+1} \epsilon_{c,t+1}) =0$, for all $a$, $b$ and $c$. Does this mean that this also applies for cases where ...
0
votes
2answers
19 views

What do we call the set of elements fixed by an involution of the second kind?

If $A$ is an algebra over a field $F$, and $\sigma:A\rightarrow A$ is an involution of the second kind, then it seems natural to talk about the set $S=\{a\in A\mid\sigma(a)=a\}$. I am not finding any ...
2
votes
1answer
30 views

What is the difference between disjoint union and union?

If $S = A \cup B$, then $S$ is the collection of all points in $A$ and $B$ What about $S = A \sqcup B$?, I think disjoint union is the same as union, only $A, B$ are disjoint. So the notation is a ...
26
votes
4answers
41k views

Difference between axioms, theorems, postulates, corollaries, and hypotheses

I've heard all these terms thrown about in proofs and in geometry, but what are the differences and relationships between them? Examples would be awesome! :)
0
votes
1answer
34 views

What does it mean for the empty set to be connected and totally disconnected?

I am trying to prove that the empty set is disconnected, but every single post I can find on this topic is about showing empty set is connected. Recall definition of connected. A set $S$ is connected ...
0
votes
0answers
17 views

“Equidecomposable”: informal meaning

I am having trouble understanding the definition of the term "equidecomposable". Is it like two sets are split into many sets and then these many sets can be joined together to make either of the two ...