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

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1answer
137 views

What is the name of this function on a graph?

I would like to know how this function is named to find how to calculate it. I have a trend like this one and want to find the upper and lower lines, the red ones (as you can see I do not have a great ...
3
votes
1answer
822 views

What is a cardinal basis spline?

Wikipedia says: the normalized cardinal B-splines tend to the Gaussian function and writes them as "Bk". Meanwhile, cnx.org Signal Reconstruction says: The basis splines Bn are shown ... ...
1
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1answer
105 views

Is the term Gaussian distribution the preferred term?

Is "Gaussian" the term preferred over "normal" when speaking of the distribution to which these names have been attached? Are they both referring to the same thing?
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2answers
137 views

How is that three-place logic operator called?

In the sources of Haskell's AwesomePrelude there is a 'bool' function with which all other operators can be defined (provided true and false are given): ...
5
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0answers
219 views

Does this property of scattered spaces have a name?

Let $K$ be a (Hausdorff) scattered topological space and for each ordinal $\alpha$ denote by $K^{(\alpha)}$ the $\alpha$th derivative of $K$ by the Cantor-Bendixson derivation (i.e., define ...
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2answers
2k views

Interpolation, Extrapolation and Approximations rigorously

A foreign book mentioned that "when the Lagrange's interpolation formula fails (for example with large sample due to Runge's phenomenon), you should use approximation methods such as ...
7
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2answers
366 views

What is the motivation for defining both homogeneous and inhomogeneous cochains?

In my few months of studying group cohomology, I've seen two "standard" complexes that are introduced: We let $X_r$ be the free $\mathbb{Z}[G]$-module on $G^r$ (so, it has as a $\mathbb{Z}[G]$-basis ...
4
votes
1answer
126 views

“belongs to” versus “contained in”

Let us consider a set $A$. let $B$ be an element of the set. Now what I want to know is that whether saying $B$ is contained in $A$ and $B$ belongs to $A$ means the same? Could anyone here cite any ...
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2answers
174 views

Is there a name for a non-iso monomorphism?

I am really bummed out to find that the term "strict monomorphism" is already used to mean something else. Can anybody console me with the knowledge that there is another name I can use for a ...
2
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0answers
72 views

Name for a Partition in which Every Block Has the Same Size

Is there a standard name for a partition of a set in which every block (i.e. the subsets comprising the partition) has the same size? Regular? Uniform? Something else? Nothing else (so I'm free to ...
1
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0answers
119 views

What is this called? [duplicate]

Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? I am looking for the name of an operation similar to factorial. Factorial would ...
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2answers
1k views

Once and for all - “Rational numbers” - because of ratio, or because they make sense?

This is a question I'm sure was asked before but I can't find it. There are many sources claiming that the term "rational number" for the elements of $\mathbb{Q}$ comes from the word "ratio", since a ...
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3answers
117k views

Which way is length and which way is width?

I hear people refer to the dimensions of things as "$2$ by $4$" etc. and I know its length by width, but I can't tell if the length dimension is vertical (up and down) or horizontal (side to side). ...
6
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2answers
183 views

History of the vocabulary for group extensions

In regular everyday English if you say something like "A was extended by B to get C", to me it means that A was in existence, B was added onto it, and now there is a larger object C. For example, ...
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1answer
245 views

Historical reason for calling $\nabla\cdot F$ divergence?

Consider the continuously differentiable vector field in ${\mathbb R}^3$: $$ F:{\mathbb R}^3\to{\mathbb R}^3,\qquad F(x,y,z)=(U,V,W) $$ where $$ U,V,W:{\mathbb R}^3\to{\mathbb R}. $$ According to ...
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3answers
2k views

Why is lambda calculus named after that specific Greek letter? Why not “rho calculus”, for example?

Where does the choice of the Greek letter $\lambda$ in the name of “lambda calculus” come from? Why isn't it, for example, “rho calculus”?
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3answers
232 views

How to define $-\infty$?

I think I understand the fundamental concept of infinity. Elementary mathematics define $\infty := \frac{x}{0}$, for every $x$. And also $\infty := \frac{-x}{0}$ for every $x$. I know only one ...
2
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0answers
123 views

Term for relation between definite and indefinite form of proof tasks

Given are two forms of one mathematical problem : (ambivalent) Find either a proof that statement S is true, or a proof that statement S is false. (definite) Find a proof of statement S. For ...
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1answer
238 views

Nomenclature in complex analysis

I am having a little confusion on the naming of functions in complex analysis. If $f$ is a holomorphic function on the complex plane and its domain is the complex plane then it's called an entire ...
1
vote
1answer
170 views

Is there any math operation defined to obtain vector $[4,3,2,1]$ from $[1,2,3,4]$?

I mean have it been studied, does it have a name? Like Transpose, Inverse, etc.. have names. I wonder if the "inversion" of the components position have a name so then I could search material on ...
4
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2answers
353 views

Is there a meaningful distinction between “inclusion” and “monomorphism”?

The title pretty much says it all. As far as I can tell, the terms "inclusion" and "monomorphism" are equivalent. (Ditto for $\hookrightarrow$ and $\rightarrowtail$.) Is this the case? Edit: ...
43
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4answers
80k 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 ...
12
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3answers
633 views

Name for $(1-x)$?

The multiplicative inverse of $x$ is $\frac{1}{x}$, and the additive inverse of $x$ is $-x$, is there a similar term for $(1-x)$?
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0answers
51 views

Name of principal root function modified to return real values if possible

Is there a concise name for the function $f_n(x)\colon\mathbb{C}\to\mathbb{C}$ which returns the principal $n$th root of $x$, except in the case when $n$ is odd and $x$ is a negative real number, in ...
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1answer
1k views

Motivation for the term “separable” in topology

A topological space is called separable if contains a countable dense subset. This is a standard terminology, but I find it hard to associate the term to its definition. What is the motivation for ...
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1answer
377 views

Principal and fiber bundles as defined by Husemoller

In his book 'Fiber Bundles' Husemoller defines principal bundles and fiber bundles quite differently from how they are usually defined. Specifically: Definition: a right $G$-space $X$ is called ...
2
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1answer
107 views

Jordan Measures without $d(A) = \sup( \{ d(x,y) | x,y \in A \} ) < \infty$?

I am trying to prove that Jordan measures satisfy with the following properties $A, B \subset \mathbb R$ and $d(A) = \sup( \{ d(x,y) | x,y \in A \} ) < \infty$, similarly for $B$: $$\bar{\mu} (A) ...
33
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2answers
2k views

How did “one-to-one” come to mean “injective”?

How did a "one-to-one" function come to mean an injective one? I find it so non-intuitive that I often have to backtrack when reading texts that use "one-to-one" because I suddenly discover that I ...
0
votes
1answer
377 views

How is called roots parts?

I'm not sure how to ask but I hope you will understand. Let's say we have such root: $$m\sqrt[2] n$$ or $$2\sqrt[2]3$$ So could you please tell me how to call m or 2 and n or 3 and how to say ...
8
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2answers
219 views

In/out equivalent to left/right “chirality”

Apologies if this is off-topic, but we're having a problem over on English Language with this question, and I thought you guys might be able to help. Basically it's a matter of topology. We know the ...
20
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4answers
10k views

What does 'linear' mean in Linear Algebra?

Why Linear Algebra named in that way? Especially, why we call it linear? What does it mean?
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1answer
143 views

Terminology for a monoid with a total ordering on the elements?

I recently came across an algorithm that works on values assuming that they are draw from a monoid equipped with a total ordering relation. I was wondering if there is a term for such a structure, ...
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2answers
2k views

What is 'an identification map'?

From Husemöller's 'Fiber Bundles' (slightly rephrased): Proposition: Consider a bundle $\xi: E \to B$, and a mapping $f: B' \to B$. Then for any $s \in \Gamma(\xi)$ there is a $\sigma: B' \to ...
3
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1answer
66 views

Library Branch Circulation Problem - Terminology and References

This is a bit general, but is there a name to this type of problem? It looks like a directed graph traversal problem, but you have multiple paths going on, and timing may be important. You operate ...
1
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1answer
102 views

Dimension and size of an array, matrix, vector

For a $1 \times n$ or $n \times 1$ vector, I remember people say it is n-dimensional. For a $n \times m$ matrix, I heard it is said to have size $n \times m$. As to its dimension, quoted from ...
1
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1answer
460 views

What is a 4-8 mesh?

A paper I'm reading uses this classification for a mesh, but I'm not sure what the numbers 4 and 8 signify. Could someone clarify? Here's an image from the paper of a 4-8 mesh.
120
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1answer
11k views

Why are rings called rings?

I've done some search in Internet and other sources about this question. Why the name ring to this particular object? Just curiosity. Thanks.
3
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2answers
1k views

name for a rational number between zero and one?

I'm searching for a unified name to convey for the concept that a number will always be between zero and one. Some info for context: in probability we've got a number between 0 and 1. Percentages ...
28
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5answers
11k views

What is the term for a factorial type operation, but with summation instead of products?

(Pardon if this seems a bit beginner, this is my first post in math - trying to improve my knowledge while tackling Project Euler problems) I'm aware of Sigma notation, but is there a function/name ...
3
votes
1answer
98 views

Name for this triangle centre

Given a triangle I draw circles around each vertex. I chose the radii of these circles so that they are all mutually tangent. There is only one way to do this. I extend these tangents. They concur at ...
1
vote
1answer
223 views

Name of the intersections of a ball with the octants?

The eight regions of space defined by the eight possible combinations of signs for $(+/- , +/-, +/-)$ for $x$, $y$, $z$ are called octants. Given a ball of radius 1 centered in the origin $(0, 0, ...
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5answers
10k views

Domain, Co-Domain & Range of a Function

I'm a little confused between the difference between the range & co-domain of a function. Are they not the same thing (i.e. all possible outputs of the function)?
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2answers
302 views

probability terminology for parameter in a Markov process

Suppose $$P(\text{feature present at time} \ t \ \text{and} \ t+\Delta t) = \beta^{2}+\beta(1-\beta) \exp(\Delta t/\tau)$$ where $\tau = 1/(\pi_{01}+\pi_{10})$. What is $\tau$?
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1answer
490 views

What is the sum of all pairwise products of a number's digits called?

I'm looking for something like this and I want to know how it's called; I'm pretty sure there is a term for it. I will show an example: Let's say we take the number 9876. ...
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0answers
104 views

Finite Levenshtein distance?

Is there a standard term for the relation on sequences where two sequences are related iff they have a finite Levenshtein distance, or for the equivalence classes it induces?
13
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4answers
31k views

What is meant by “evenly divisible”?

"What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" Is it different from divisible?
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1answer
102 views

2D transformation without rotation

Is there a name for 2D transformation with the least squares adjustment having the following parameters: shift_x, shift_y, scale. Transformation does not use any rotation... Thanks for your help.
10
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1answer
487 views

Is there a term for an “inverse-closed” subring of a ring?

I would like to know whether there are established terms for A subring $S$ of a ring $R$ such that $S \cap U(R) = U(S)$; in other words, every element of $S$ which is invertible in $R$ is invertible ...
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2answers
879 views

Meaning of “a mapping factors over another”?

I was wondering what "a mapping factors over another mapping" generally means? Does it have something to do with commutative diagram in category theory? I have seen this usage in different ...
1
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2answers
611 views

Strictly convex at

Another terminology question: If a function $f(x)$ is strictly convex at $y$, does this mean, for an already convex function: a) $f'(y) = 0$, or equally, $y = \arg \min_y f(y)$ b) ...