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

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1answer
7k views

Coterminal Angles?

I understood coterminal angles as angles that have the same terminal angle value. By this logic, why aren't 135 and 315 coterminal? They both have a terminal angle of 45. Is my interpretation of ...
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1answer
510 views

Ideals in non-associative rings and the identity $(xy)z=y(zx)$.

I have come across this paper. The authors prove that magmas satisfying the identity $$(xy)z=y(zx)\tag1$$ are nearly both associative and commutative. To be precise, they show that in such magmas, ...
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1answer
585 views

Meaning of “Radial Separation”?

I'm reading conflicting uses of the term "Radial Separation." On this math forum it is implied to be "the distance between circles" as well as "the distance between the circles of the spiral". A ...
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3answers
109 views

Does the operator $\sum_i x_i \frac{\partial}{\partial x_i}$ have a name?

This appears in Euler's homogenous function theorem. Does it have a commonly-used name?
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3answers
1k views

What does a space mean?

In Wikipedia, they say that a space is a set with some added structure. But what do they mean by "with some added structure"?
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1answer
132 views

Terminology for implication of theorems

In Portuguese, the following is considered the accepted terminology for the implication of theorems: $$\text{Theorem:}\\ \text{Hypothesis } \Rightarrow \text{ Thesis}$$ Hypothesis is the antecedent ...
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1answer
109 views

Range Terminology

How should the following statement be interpreted: Let $f$ be a function with range in* $[0,1]$. (Here the word "in" has been deliberately included.) In this context, the range is the same as the ...
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1answer
610 views

General definition of growth in mathematics

From high school math one knows "linear growth", "exponential growth", "logistic growth", "bounded growth" etc., but is there a common accepted general definition of "growth" which covers the special ...
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1answer
455 views

What are the rings in which left and right zero divisors coincide called?

A unital ring $R$ is reversible iff $ab=0\implies ba=0.$ This condition implies the following one. If $a\in R$ is a left-zero divisor, then $a$ is also a right-zero divisor. And the other way ...
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1answer
276 views

Name of probability distribution

Does this distribution have a name: $f(x) = yx^{y-1}$ for $0 < x<1$ and $y>0$? It looks like an exponential distribution. Or is it a nameless distribution?
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1answer
150 views

Bernoulli Distribution with support different from $\{0,1\}$

Suppose the support of a distribution is $\{12 , 13 \}$ with $P(X = 12) = p$ and $P(X = 13) = 1-p$. Is this still a Bernoulli distribution even if the support is not $\{1, 0 \}$?
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1answer
548 views

Why bifunctors?

Why are bifunctors called "bifunctors"? They are just functors, are they not? After all, we don't call functions of two arguments "bifunctions", or natural transformations with two parameters "...
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2answers
359 views

When does “pairwise” strengthen and when does it weaken?

"Pairwise disjoint" is stronger than "disjoint"; it sometimes happens that $\displaystyle\bigcap\limits_{i\in I} A_i=\varnothing$ but for every $i,j$, or at least for some, one has $A_i \cap A_j\ne\...
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1answer
494 views

What is generic rank?

What is meant by generic rank of a matrix? Is it something different from the rank, and does the word generic has just its English meaning? I came across this term in the book "Algebraic statistics ...
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1answer
2k views

Cluster point of a function at a point

This post is quite long, since I wanted to include the necessary context. (Maybe I've put there too much.) Maybe you might prefer to look at the questions at the end of this post, first. $\...
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0answers
116 views

Given an Associative Operation on an Infinite Set, How Many Similar Operations are There?

With respect to an operation $O_n$ on an infinite set, define a mimic operation $O'_n$, as an operation which differs from $O_n$ only by a finite number of points, and a $k$-mimic operation $O^{k}_n$ ...
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1answer
302 views

Name of distance from center to side of rectangle

Is there a special name for the distance from the center of a rectangle to a side? I haven't done geometry in a while, but I thought there was an equivalent of a "radius" for regular polygons.
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1answer
200 views

simplex and power set

I read the following: Let $M$ be a set. The simplex on $M$ is the set of all subsets of $M$; we denote this by $\Delta_M$. We will sometimes refer to the elements of $M$ as vertices of $\Delta_M$. A ...
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1answer
318 views

Name of a Euclidean Geometry Theorem

There is a well known theorem in plane Euclidean geometry as follows, and I would like to know only the name by which it is known. Theorem: Let $ABC$ be a triangle. Choose points $D,E,F$ on the ...
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0answers
51 views

Set of “rounded to nearest p” fixed decimal numbers?

I'm trying to define a set of "fixed precision" or "rounded" numbers. For example, I want to define a rotation in degrees by every $5$ degrees, so $X = \{0,5, \ldots , 355, 360\}$. $$X = \{x_i \in \...
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1answer
366 views

Set terminology and symbols in optimization

Coming from engineering background, I'm getting a little lost in terminology and symbols, but I still want to be mathematically precise. In engineering optimization, I often have say two design ...
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3answers
3k views

If “multiples” is to “product”, “_____” is to “sum”

I know this might be a really simple question for those fluent in English, but I can't find the term that describes numbers that make up a sum. The numbers of a certain product are called "multiples"...
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1answer
436 views

Was the definition of $\mathrm{erf}$ changed at some point?

I have seen two competing definitions of the error function. When I was an undergrad, Spiegel's Mathematical Handbook of formulas and tables (mine is the 1968 edition) was the definitive authority, ...
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1answer
639 views

Is there a name for a neither-increasing-nor-decreasing-but-alternating sequence like below?

A sequence of at least two distinct integers ${ \left\{x_1, x_2, x_3, x_4, \ldots, x_n | n \geq 2, x_i \ne x_j \forall i \ne j \right\} }$ that satisfies either the property: $$ x_1 < x_2 > x_3 ...
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2answers
420 views

Proper name or term of comma thousandths grouping notation

What is the proper name or terminology of notation for using a comma to separate and group thousandths of a number? As in, formatting large numbers for readability: ...
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5answers
12k views

Use of “without loss of generality”

Why do we use "without loss of generality" when writing proofs? Is it necessary or convention? What "synonym" can be used? Thanks.
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2answers
3k views

Is equality the same as identity?

An identity is a relation that means that whatever the number or value may be, the answer stays the same. But is it possible to have equality without identity?
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0answers
87 views

Definition of fragility

What does it mean for a solution to a system of differential equations to be fragile? A context for the term can be found here: This is taken from here in Mathematical Methods for Mechanics: A ...
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3answers
16k views

Why does an infinite limit not exist?

I read in Stewart "single variable calculus" page 83 that the limit $$\lim_{x\to 0}{1/x^2}$$ does not exist. How precise is this statement knowing that this limit is $\infty$?. I thought saying the ...
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1answer
103 views

Is there a term for the “opposite” location in a matrix?

I'm just looking for the correct term to describe a concept: Suppose I have a 5x5 matrix: A B C D E F G H I J K L M N O P Q R S T U V W X Y I can pick any two cells, let's say the cells I and Q, ...
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1answer
63 views

Order of operations term

What is the single-word term for "order of operations" in English, if there is one of course? I am debating this with colleague and we don't know if such term exists in English math literature. Thank ...
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2answers
256 views

terminology: what is meant if someone writes “calculus of ..”?

This question might be a little soft as it does not have a definite answer, so I hope I do not break the conventions of this forum by posting it here. I have now come across the term "calculus of ...
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1answer
196 views

What set operation is this?

Given two sets $ A = \{\{1\} , \{2 , 6\} \}$ and $ B = \{\{2\} , \{3\} , \{4 , 5\} \}$, what set operation can produce $$ C = \{ \{ 1 , 2 \} , \{ 1 , 3 \} , \{ 1 , 4 , 5 \} , \{ 2 , 6 , 2 \} , \{ 2 , ...
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0answers
78 views

Is there a name for a set together with a unary operation?

Is there a name for a set together with a unary operation? If so, where can I learn more about them? Is there anything interesting about them? Are they simply a special case of groups? It simply ...
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1answer
1k views

What does “by what part” mean?

I have a homework problem that is asking me for something. Here's the last line quoted: If you switch to the ring, by what part will you decrease the electric field magnitude at P? Okay, so the ...
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2answers
187 views

Why is the permutation matrix called so? Any combinatorial meaning?

My question is very simple but I cannot really have it answer. Why the permutation matrix is called permutation matrix?? Is there any combinatorial meaning with the permutation matrix? (As I know, a ...
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2answers
3k views

Casio Calculators Give 2 Different Answers [duplicate]

Possible Duplicate: What is 48÷2(9+3)? Sorry if this has already been asked, my searches were fruitless... There's been a buzz lately about the different results given by two different ...
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3answers
151 views

Name of the set $\{x : x_1 \leq x_2 \leq \cdots \leq x_n\}$?

I was looking for a standard name of the set $\{x \in A : x_1 \leq x_2 \leq \cdots \leq x_n\}$, where $A = [0,1]^n$ or $A = [0,\infty)^n$. I think I saw this recently, but now I cannot find it ...
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2answers
533 views

What is a fancy way to say “same sign” for two numbers?

If $xy > 0$, then $x$ and $y$ are [insert fancy smart term for same sign] Does "sign parity" work here?
3
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1answer
850 views

What is the proper name of a “doughnut sector” or “curved trapezoid”?

What is the name of this shape? It is basically a sector with a doughnut hole cut out of it. Just wondering if it has a proper name.
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6answers
3k views

What is the opposite of a cross term?

When we multiply out $(x + y)(x + y)$, we refer to the two $xy$ terms as "cross terms". Is there a corresponding term for the $x^2$ and $y^2$ terms?
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3answers
236 views

What was this theorem called

Back at the university we have proven (lot of work) that if $$S(X)C(Y)+C(X)S(Y) = S(X+Y)$$ and $$C(X)C(Y)-S(X)S(Y) = C(X+Y)$$ then $S(X)$ is $\sin(x)$ and $C(X)$ is $\cos(x)$ (or constant $0$, meh). ...
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1answer
633 views

Empty set as a relation

The empty set is an $n$-ary relation for every $n$, right? How should we call a pair $(n;r)$ consisting of some number $n$ and an $n$-ary relation $r$? To specify $n$ is necessary only when $r$ is ...
12
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1answer
2k views

What are curves (generalized ellipses) with more than two focal points called and how do they look like?

An ellipse is usually defined as the locus of points so that sum of the distances to the two foci is constant. But what are curves called which are defined as the locus of points so that the sum of ...
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1answer
59 views

Math vocab: operator on $S$ and into $S =$?

Is there a special name for a binary operation on the set $S$ that is also into $S$, that is unambiguous with other uses. I.e. if it's "operator on $S$", I've heard that in other places meaning the ...
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1answer
186 views

What does Tarski mean by a “tautological operation” on a Boolean algebra?

I am reading Part II of Chin and Tarski's "Distributive and Modular Laws in the Arithmetic of Relation Algebras". In the beginning of section 4, the authors say "In general, if $\odot$ is a binary ...
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2answers
1k views

Why are harmonic functions called harmonic functions?

Are they related to harmonic series in any way? Or something else? Wikipedia didn't help.
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1answer
773 views

What does it mean for a function to be bounded near $\infty$?

Suppose $f(z)$ is some analytic function which is bounded near $0$. Then $f(1/z)$ is bounded near $\infty$. What exactly does that last statement mean practically? Does it mean $|f(1/z)|$ is bounded ...
3
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0answers
357 views

Etymology of the word “pole”?

In his book Control System Design, Bernard Friedland writes (section 4.2, page 115): The roots of the denominator [of a rational function] are called the poles of the transfer function because $H(...
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2answers
346 views

Notation for covariant derivative

I'm reading John M. Lee's book " Riemannian Manifolds". On page 57, the covariant derivative of $V$ along a curve $\gamma$ is defined, where $V$ is a vector field along $\gamma$. It is denoted by $...