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

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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
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0answers
10 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 ...
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1answer
35 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 ...
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1answer
34 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 ...
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1answer
16 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 $ ...
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0answers
30 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 ...
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2answers
32 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. $$97+198$$ $$=(100-3)+(200-2)$$ $$=(100+200)+(-3-2)$$ ...
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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?
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0answers
45 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
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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 ...
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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 ...
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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} ...
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1answer
50 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 ...
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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 ...
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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 ...
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1answer
30 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) = ...
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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 ...
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2answers
28 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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."?
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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?
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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 ...
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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 ...
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3answers
150 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 ...
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2answers
26 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 $n$ ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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
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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 ...
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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 ...
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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! :)
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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 ...
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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 ...
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0answers
23 views

Where does the name of the hypergeometric distribution come from?

I understand what it does and how to get there, but why is it called hypergeometric? All the other distributions I know of have rather self-explanatory names like "binomial" or "exponential", or are ...
0
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1answer
25 views

If I subtract a number (from a sequence) from the average of all the numbers in that sequence - what do I have?

If I have a number (from a sequence) and I then subtract that number from the average of that sequence- what do I have? I would describe it as a 'deviation from the average' - but is there a better ...
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4answers
779 views

What is linearity? [duplicate]

Once someone asked me the question "What is linearity?" in a proficiency exam. I went hot and cold all over. Although, I heard and even used the term linearity many many times, I had not really ...
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3answers
371 views

What does echelon mean?

When you solve a system of linear equations, you write down the augmented matrix and reduce this to reduced row echelon form. What is the meaning of the word echelon?
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14 views

Characteristic polynomial of a graph and structure function of a graph?

The characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. It is a graph invariant, though it is not complete: the smallest pair of non-isomorphic graphs ...
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1answer
44 views

What is this kind of cone called?

Consider the following cone: Assume a circular base (but I don't think that's really critical to my question). Note that the line connecting the vertex of the code to the plane of the base, where ...
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4answers
74k views

What are the numbers before and after the decimal point referred to in mathematics?

Sorry for asking such a basic question - but is there an actual term for the numbers that appear before and after the decimal point? Example: 25.18 I know the 1 ...
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2answers
83 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.
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2answers
56 views

why are equivalence relations called so?

"an equivalence relation is the relation that holds between two elements if and only if they are members of the same cell within a set that has been partitioned into cells such that every element of ...
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0answers
3 views

Name for a complex but consistently wound polyline loop?

So I have an algorithn which operates on a plane region defined by a directed polyline loop. This algorithm has the unusual property of working properly for self-intersecting polylines, but only if no ...