Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [terminology]

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

Terminology is a discipline that studies, among other things, the development of terms and their interrelationships. This tag is intended to be used for questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

8534 questions
3
votes
4 answers

Mathematical French: étant - does it introduce an assumption or a fact

What does the form étant mean in the following sentence, excerpted from an article by E. Szpilrajn: "La fonction $f_e$ étant mesurable $(K)$, tous les ensembles de la suite $e$ et leur complémentaires appartiennent à $K$." Does it mean: "$f_e$…
Evan Aad
  • 11,422
3
votes
5 answers

Math definition for "positive or negative"

If you define a direction on a plane as either positive or negative, what would you call its positive/negativeness? Its orientation? I feel like there is a better word out there for this. So like, if there is an arrow that starts at (0,0) and has…
Soo
  • 901
3
votes
0 answers

Flow Diagram of Formulae to Create Algorithm - Does this Method have a Name? Does it have Software?

This is a diagram that I recently created to help me solve a series of formulae in order to create an algorithm for a database program. For some reason I just couldn't visualise all the elements, so I decided to write it out to see what I could…
Excrubulent
  • 131
3
votes
1 answer

Elementwise vs componentwise vs coordinatewise vs pointwise

I am programming a basic mathematical library that deals with vectors, matrices, tensors, holors, functions, etc. I am wondering what the best terminology will be regarding pointwise/componentwise/etc operations (or maybe I should even call the…
lightxbulb
  • 2,047
3
votes
2 answers

What is meant by "passing to a subsequence"?

Let $\{f_k(x)\}_{k=1}^\infty$ be a sequence of differentiable functions defined on $[0,1]$. Suppose $f_k(0)=0$ and $|f_k'(x)|\le M$ for all $x\in[0,1]$ and for all $k\ge1$. Prove that after passing to a subsequence, $f_k$ converges uniformly on…
zbrads2
  • 1,054
  • 6
  • 13
3
votes
2 answers

"Dimension of a vector" vs. "Directions of a vector"

A vector like $(7,5,4)$ is said to have the dimension of 3. But I have also heard that the "5" is the "second dimension of the vector". In the later case one would say the vector has three dimensions (plural). What is the correct way of…
Make42
  • 1,085
3
votes
2 answers

Is there a name for functions $f:\mathbb{R} \to \mathbb{R}$ such that whenever $|a - b| < |b - c|$ we have $|f(a) - f(b)| < |f(b) - f(c)|$?

Is there a name for functions $f : \mathbb{R} \to \mathbb{R}$ such that whenever $|a - b| < |b - c|$ we have $|f(a) - f(b)| < |f(b) - f(c)|$? It seems like this property should be related to convexity. The above definition was my attempt to make…
Charles Hudgins
  • 5,649
3
votes
3 answers

Terminology: elegant proofs

What do mathematicians mean when they say: that's an "elegant proof" of such and such. What are the ingredients of an elegant proof? Maybe you can give examples of elegant proofs of your own.
mrk
  • 3,075
3
votes
6 answers

How to express inequality between variables?

I have variables $a, b, c, d \in N^+$, how do I express the condition that all their values must be different? Also, what field of mathematics covers ways of expressing constraints? I couldn't even find an adequate way to tag this question.
pwned
  • 447
  • 5
  • 10
3
votes
2 answers

Solving $bxy+cy-ax=0$ - NOT the roots

I am looking for a bit of terminology but all I can ever find is explanations for finding the roots of equations, which is not what I am after. Simply put, suppose we have a rational function, such as $y=\displaystyle{\frac{ax}{bx+c}}$ and suppose…
user492494
  • 53
3
votes
2 answers

When not specified, what is the meaning of "not equals"?

When talking about quantities that vary, does $\neq$, by default mean "is always not equal to" or "is not always equal to"? The context of this is the following question: We're having a dispute over the meaning of the $\neq$ in the absence of a…
Manishearth
  • 1,050
3
votes
5 answers

In the expression sqrt("cat"), what is the formal name of "cat"?

This is more of a semantic question than an actual math question but I couldn't see where better to put it. If I would write a silly equation like the aforementioned $ \sqrt{"cat"} $, what is the proper name for the "cat" portion? Can one say it's…
CodyBugstein
  • 1,642
3
votes
1 answer

"there exists" vs. "there is"

Is the difference between "there exists" and "there is" purely stylistic? The book I am using uses "there is" the majority of the time, except for very few cases of "there exists," so I wanted to make sure.
tmakino
  • 697
3
votes
0 answers

Terminology for functions whose slopes have the same sign?

Given functions F and G, where the slope of F has the same sign as the slope of G. What is the correct terminology for the relationship between these two functions? Note that there might not be a constant multiple factor that maps the slope of one…
Gili
  • 151
  • 5
3
votes
0 answers

Etymology of symbols $\in$ and $\varnothing$

I read many years ago in somewhere (I don't remember where) that the symbol $\in$ for membership of sets comes from Greek word "$\epsilon\sigma\tau\iota$" meaning "is in". So $a\in A$ means $a$ is in $A$. It it right? If is so, then what about…
Qurultay
  • 5,224
1 2 3
…
49 50