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

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3
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3answers
4k views

Bilinearity: what does it mean?

What does bilinear really mean? Everytime I heard the word, I think it should be "linear in 2 ways?" For example, from the definition of inner product (taken from Appendix A of "Wavelets For ...
0
votes
1answer
108 views

What is the total X,Y coordinate on a grid called?

Say I have a grid that is 4 columns wide, 4 rows high, I can get the "total" number of a certain point like this: (y * width) + x So point (0,1) would be ...
6
votes
5answers
6k views

Is there a formal name for an equation that has no solution?

I was wondering if there is a formal name for the equations which don't have any solution? For example consider this equation in $m$ : $$ -2(3-m)+15=6m-4(m-20)$$ If we do the algebra we will get ...
1
vote
4answers
267 views

What is the name of a function that changes the sign of a number?

What is the function called, when the function effectively multiplies its input by $-1$? i.e. $f(x) = -x$. Similar terminology being the inverse of a number, i.e. $f(x) = 1/x$. There may not be ...
5
votes
4answers
3k views

On the Origin and Precise Definition of the Term 'Surd'

So, in the course of last week's class work, I ran across the Maple function surd() that takes the real part of an nth root. However, conversation with my professor ...
2
votes
0answers
52 views

Name for this type of space over a boolean algebra?

The structure has two carrier sets $E$ and $A$, operators $({}^*, \wedge)$ over $E$, and a ternary "decision" operator $D:E \times A \times A \to A$, written infix $(p?a:b)$, whose intended meaning is ...
0
votes
1answer
22 views

Final Error of two module in serial and parallel

Suppose we have two modules in serial call them $M_1,M_2$ , a signal passing from $M_1$ to $M_2$ has probability of error $\epsilon_1$ , and at $M_2$ has $\epsilon_2$ probability of error. In serial ...
11
votes
3answers
7k views

Root or zero…which to use when?

This may seem like a very basic question, but: What exactly is the difference between a root of a polynomial, and a zero? Of course I realise that they are technically exactly the same thing, but ...
3
votes
3answers
119 views

Is there a formal name for a mathematical model that has an overly sensitive parameter

I'm a software engineer with a bit of mathematics expertise working with an NGO that has developed mathematical models for ecosystem services. It turns out that one of these models is overly ...
3
votes
0answers
476 views

algebraic ternary operators

In the analysis of certain Natural Language Processing queries, there is a certain algebra that arises with a ternary operator over a group with the following two properties: $$ ( ( a , b , c ) , d , ...
1
vote
3answers
191 views

What is the proper term for a function where domain and codomain coincide?

What is the proper term for a function where domain and codomain coincide? E.g. in programming languages a function f : Int => Int or f : Double => Double. Thanks.
2
votes
1answer
162 views

The reason for different terminologies

Different authors seem to have different conventions when they define the term affine variety (similarly projective variety). For the purposes of this question let us stick with the affine case, and ...
5
votes
3answers
3k views

Can the word “derive” be used to mean “take the derivative of”?

Back when I was in high school, the usage of the word "derive" to mean "take the derivative of" was really widespread. It always bothered me because I felt that the proper verb should be ...
15
votes
1answer
595 views

Polarization: etymology question

The polarization identity expresses a symmetric bilinear form on a vector space in terms of its associated quadratic form: $$ \langle v,w\rangle = \frac{1}{2}(Q(v+w) - Q(v) - Q(w)), $$ where $Q(v) ...
1
vote
1answer
51 views

Would it be appropriate to use “power” to describe an $n$-fold fold of a number with some associative binary operation? Is there a better expression?

What I mean are expressions like $$ \underbrace{a\cdot a\cdot\ldots \cdot a}_{n}. $$ When $(\cdot)$ is multiplication this obviously is the $n$th power of $a$, when it's addition it's an $n$-fold ...
4
votes
2answers
98 views

Name of all subsets of a certain size

Let's say I have a set $S$ and I want all subsets that have two elements. Is there a special name for that? To put it another way, I want to know if there is a name of the subset of a $S$'s power ...
1
vote
0answers
31 views

Name this concept: Comparing equal sized vectors vs. comparing features

If you obtain a vector by taking $n$ discrete samples over some underlying function, then it's easy to compare that vector with another of the same size. With a bunch of $n$-dimensional vectors, you ...
2
votes
1answer
652 views

Base versus basis

This is a question on the borderline between mathematics and English. I wonder in mathematics, are there some general differences between concepts with base and with basis in their names? In other ...
4
votes
1answer
77 views

Nomenclature for distributive action between semigroups

Let $(G,*)$ and $(H,+)$ be semigroups. Let $\cdot$ be an action of $G$ on $H$, such that $\cdot$ distributes over $*$. [I.e., $(g_1 * g_2) \cdot h = g_1*(g_2\cdot h)$, and $g\cdot(h_1+h_2) = (g\cdot ...
5
votes
1answer
242 views

Is “converges at” idiomatic English in some regions?

Some students write, e.g., "$\sum(1/n^2)$ converges at $\pi^2/6$", where I would write "converges to". Are there regions of the English-speaking world where it is standard to say "converges at"? Or ...
2
votes
1answer
121 views

Shellable and Graphs

Suppose we have a graph $G$ of order $n$. Also suppose that we form the coloring complex $S(G)$ of $G$. What does it mean when we say that $S(G)$ is shellable?
1
vote
1answer
377 views

What is the terminology for converting a list of numbers into a particular range?

Say for example I have a list of n numbers. I would like to convert this into another list of n numbers which are all within a certain range, e.g. 0 and 1, but still maintain the relationship between ...
3
votes
1answer
142 views

When a Permutation is not a cycle

$\sigma = \pmatrix{1&2&3&4&5&6&7&8\\3 &8 &6 &7 &4 & 1 & 5 & 2} = (136)(28)(475)$ I just have a question about terminology. Would it be correct ...
1
vote
1answer
153 views

Essentials of Plane Geometry: Need Help Understanding Wording of Question

Could someone explain to me what this simple problem is asking me to do? Draw three straight lines intersecting by twos? Does this mean that each line in the set of three has to be intersected ...
0
votes
1answer
34 views

Terminology concerning a certain solution to a certain system of equations

Say you have a solution $\textbf{x}=(x_1,x_2,\ldots,x_n)$ to a system of equations. It turns out that $-\textbf{x}$ is also a solution. Is there accepted terminology for such a pair of solutions? (I ...
3
votes
3answers
924 views

Orbit vs. Cycle

Can someone explain to me the difference between an orbit and a cycle?
6
votes
2answers
373 views

If $f''(x)=0$ but is not an inflection point, what is it called?

If the second derivative of a function $f(x)$ equals zero at point $x_0$ ( $f''(x_0)=0$ ), the point is an inflection point if the concavity changes. Here's an example of an inflection point. ...
1
vote
4answers
457 views

What is the name for a maximal convex set of points contained in another set of points?

What is the name for a maximal convex set of points contained in another set of points X? Maximal in terms of inclusion. For the desired set to be unique, X can be restricted to be a simple polygon ...
2
votes
1answer
120 views

Eccentricity of a vertex

Eccentricity of a vertex $v$ in a graph $G$ is defined as max $\{d(v,w):w\in V(G), w\ne v\}$. My question is why is the word eccentricity used, what is the reason? Thanks
6
votes
2answers
696 views

Mathematical versus computer “Dynamic Programming”

I heard the term "dynamic programming" and naively assumed it had to do with programming in the sense of computer programming (as that's the only way I've heard the word used before. Used to work ...
2
votes
1answer
149 views

What is a relatively bound variable?

edit: Interestingly, the authors also state at one point that the choice of introduction rule is determined by the structure of the previous goal and the list of introduction rules; but at another ...
2
votes
2answers
768 views

Why we call it technological coefficients?

I'm learning linear programming's basic concepts. In following inequality: $$ \begin{align} \text{Minimize }c_1x_1 + c_2x_2 + \cdots+ c_nx_n \\ \\ \text{Subject to }a_{11}x_1 + a_{12}x_2 ...
1
vote
1answer
968 views

basis/test/Ansatz functions: difference?

Literature on numerical analysis using approximation of functions via projection into finite-base function space uses terms test function, Ansatz function, basis function. What is the difference? My ...
11
votes
1answer
708 views

Why is $i$ called “imaginary”?

I was reading this question, and, after reading the responses, I felt like I had a much better understanding about how they're just another type of number definition. Why, then, are they called ...
11
votes
2answers
273 views

What is the difference between probability and statistics?

Is it that probability is top-down (going from pure distributions to predictions about events) and statistics is bottom-up (going from specific events to predicting pure distributions?) I'm pretty ...
5
votes
1answer
176 views

Sorting through “algebra of random variables,” vs. “probability space,” etc

I have been reading through Wikipedia pages, and I'm still really confused. What is the difference between "algebra of random variables" and "probability space."? Are they just different words for ...
5
votes
1answer
2k views

What does it mean by the order of a group?

show that the relations $a^4=1$, $b^2=a^2$, $b^{-1}ab=a^{-1}$ define a group of order 8. This is a homework problem I got. I don't understand what they mean by 'a group of order 8', because I ...
6
votes
1answer
392 views

What is the term for the projection of a vector onto the unit cube?

Normalizing a vector sets its magnitude to $1$ and retains its direction. In three dimensions, it projects the vector onto the unit sphere. Is there a term associated with projecting it onto the ...
2
votes
1answer
177 views

Does this matrix have a name?

If $L$ is a lower triangular matrix of ones, does the following matrix have a special name? $$A = \left(\begin{matrix}L & -L \\ -L & L \end{matrix}\right)$$
1
vote
2answers
635 views

What to call the expressions that are not polynomials

The following expressions in examples aren't polynomial expressions: $$2x^2-5x+(3/x)$$ $$9- \sqrt x$$ Neither they are rational expressions, I've been just told that by book. but then what do you ...
10
votes
1answer
1k views

Why is it called a 'ring', why is it called a 'field'?

The definitions of 'ring' and 'field' are pretty straightforward. For a ring (e.g. integers): addition is commutative $( 1 + 2 = 2 + 1 )$ addition and multiplication are associative $(2 +(2+2)) = ...
2
votes
2answers
380 views

Confused about Wikipedia definition of NP

I've been checking my understanding of the definitions of NP and NP-complete and I am confused by some of the definitions given on Wikipedia; for example, the article about NP-complete describes NP ...
0
votes
1answer
397 views

Is it correct to say that $P=NP$ implies $P=NPC$?

Is it correct to say that $P=NP$ implies $P=NPC$? I was reviewing the definition of NP-complete and I noticed this diagram which states that if $P=NP$, then $P=NP=NPC$. However, it seems to me that ...
3
votes
1answer
926 views

What does height of an algebraic equation mean?

I want to solve this question but I don't understand what "height" of an algebraic equation is: Find the number of solutions of the set of all algebraic equations of height 2.
22
votes
3answers
2k views

Why algebraic topology is also called combinatorial topology?

I remember reading somewhere(at least more than once) that algebraic topology is also known by the name "Combinatorial Topology" which essentially tags the subject fundamentally with some counting ...
1
vote
1answer
104 views

What's the name of a submanifold-plus-any-missing-boundary?

Is there a standard name for the closure of a submanifold of some fixed manifold M? Example. The closed interval [0, 1] is not a manifold, because there is no atlas which contains charts at ...
4
votes
2answers
442 views

Name of property describing the number of times a function changes concavity?

For example, $f(x)=\sin x$ changes concavity an infinite number of times, $f(x)=x^3-x$ has two regions of concavity (changing concavity once), and $f(x)=x$ changes $0$ times. Is there a name for ...
2
votes
1answer
45 views

Is there a name for a position on a function surface and the value at that position?

Is there a name for a position on a function surface and the value at that position? E.g., if I have the function $f(x,y) = x^2 + y^2$, and I know that at the point $(2, 2)$ it evaluates to $8$, is ...
1
vote
2answers
447 views

What is the generalization of 'theorem' and 'conjecture'?

What is the most specific word that describes both? As in "all theorems and conjectures are ..." ?
0
votes
1answer
517 views

doubt on iid distribution vs uniform distribution

I am a bit confused when I read "iid distribution". It looks to me like what is called "uniform distribution" i.e. a distribution of probability that is constant in a range. Am I correct in thinking ...