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

learn more… | top users | synonyms (2)

0
votes
1answer
34 views

Is it appropriate to refer to the “height” of a function?

I need to point out that a certain process will have an effect on the average "height" (i.e.: the average value of the function in the y axis) of a 1-dimensional function. Is it correct to say that ...
0
votes
1answer
24 views

Is a gradient system considered an ODE or PDE?

When you have a system of the type $$\dfrac{dx(t)}{dt} = \nabla V(x)$$ Is this considered an ODE or a PDE? Because you have a single derivative with respect to $t$ on the lefthand side, whereas on ...
2
votes
2answers
35 views

Is there a name for the way I am averaging the cost of cards?

My buddy and I were discussing different ways of deciding how much mana to include when constructing a deck. Without thinking much about it I used a method of finding the average converted mana cost ...
0
votes
0answers
27 views

Do global extrema of functions also happen on critical points?

Do global extrema of functions also happen on critical points? The wikipedia page says the theorem holds for all local extrema. But does it hold for globals too? Or are globals also considered locals ...
0
votes
1answer
44 views

What axiom in Math says “similar inputs should yield similar outputs”?

It is easy to take for granted the simple idea that similar input $x$ to a function $f(x)$ should yield similar outputs - such that if the difference between $x$ is arbitrary small, then we should ...
0
votes
0answers
20 views

Is it acceptable to call curves on parametric surfaces “isoparms”?

Let $\mathbf{r}(u,v):[a_0,b_0] \times [a_1,b_1] \to \mathbb{R}^3$ be a parametric surface. If $u$ and $v$ are fixed, is it allowed to call $\mathbf{r}(u,\cdot)$ and $\mathbf{r}(\cdot,v)$ "isoparms" or ...
1
vote
0answers
21 views

Does this partition of an indexed union have a standard name?

Let $\mathscr{I}$ be an arbitrary index set, and $\{A_i : i \in \mathscr{I}\}$ be a family of sets indexed on $\mathscr{I}$; $U = \bigcup_{i \in \mathscr{I}} A_i$; $\phi: U \to \{0, 1\}^\mathscr{I}, ...
0
votes
0answers
13 views

Name of this class of functions

How is a continuous and monotonic function called, that for a bounded input (e.g. $0..1$), generates results from $0..\infty$? As an example of where Im going: A similar class of functions, that goes ...
7
votes
2answers
158 views

Is there a name for an 'incomplete' factorial $\frac{n!}{m!}$?

I noticed I was computing $${n! \over m!} ,$$ where $n > m$, inefficiently, as $$\frac{\prod_{k=1}^{n} k}{\prod_{k=1}^m k},$$ when many terms cancel out and I could just be calculating ...
2
votes
1answer
42 views

Name of a particular category

I'd like to work with a certain category which seems classic to me, but I don't know its usual name. Let's define $$Ob(\mathcal{C}) = \{(Y,Y_1,Y_2,f) : Y = Y_1 \cup Y_2, f : Y_1 \to Y_2\},$$ where ...
1
vote
1answer
18 views

Permutation of rows with repetition

A binary matrix with exactly one entry of 1 in each row and 0s elsewhere performs a "permutation with repetition" of the rows of the matrix it left-multiplies. Example: $$ \begin{bmatrix} 1 & 0 ...
2
votes
1answer
29 views

What is the closure of $A = \{x| 1<\|x\|<3\} \cup \{(0,0)\}$ and why am I wrong?

Given $A = \{x| 1<\|x\|<3\} \cup \{(0,0)\}$ Find $\bar A$ My hunch is $\overline A = \{x| 1 \leq x \leq 3\} \cup \{0,0\}$, but my friend says I am wrong, the closure of $A$ must ...
3
votes
0answers
62 views

Is there a connection between the “independent sets” in matroids and “independent sets” in graph theory?

I've been reading up on matroids recently, which are used in the theory of greedy algorithms. A matroid is a pair $(X, I)$ where $X$ is a set and $I \subseteq \wp(X)$ is a family of sets over $X$ ...
0
votes
1answer
34 views

On “bounded” in intuition for a theorem involving autonomous 1st-order ODEs

Suppose we have an autonomous first-order ordinary differential equation $$\frac{dx}{dt} = f(x) \tag{*}$$ where $f$ is continuously differentiable for all $x \in D \subseteq \mathbb R$ s.t. the ODE ...
0
votes
1answer
64 views

$K$-monomorphism that is not $K$-automorphism?

I am confused by the terminology where $K$ precedes terms such as $K$-monomorphism and $K$-automorphism in Galois theory. I am trying to come up with a simple example about $K$-monomorphism that is ...
1
vote
3answers
79 views

Simple algebraic equation that needs solution $x = x - 1$

$x = x - 1$ ; is it undefined or indeterminate? $x - x = - 1$ $0 = -1 ; 0 $ is not equal to $-1$. but an equation is an equation, as there should be a number when substituted to $x$ when subtracted ...
0
votes
1answer
30 views

How to read the Jacobian (determinant) shorthand notation, and why is it so cryptic?

Lets say we have a function $f : \mathbb{R}^3\rightarrow \mathbb{R}^3$, as defined below, with its value being denoted as $(a, b, c)$ for convenient reference. $$f(x,y,z) = (x^2, y^2, z^2) = (a, b, ...
0
votes
0answers
14 views

What term describes measuring the shortest distance from an inside object's perimeter to a containing outside object's perimeter?

Given two closed curves where the first curve is completely inside the second curve, what term describes the minimal distance to travel from the inside curve to the outside curve? For example, in the ...
4
votes
1answer
62 views

Why are function definitions not written with the := sign

Why are function definitions not written with the $:=$ sign instead of the $=$ sign. It seems to me that $:=$ would be more intuitive and avoid a lot of unnecessary ambiguity. Consider the following ...
3
votes
2answers
58 views

Is the Laplace transform essentially a generalized version of the Fourier transform?

My current understanding of the two concepts is far from perfect, and I am essentially just a beginner. But it seems to me that while the Fourier tries to decompose functions as a composition of ...
1
vote
1answer
50 views

What are my polynomials called? (and where can I read about them)?

I've run across some polynomials that are natural enough I imagine must have been named and studied, but don't know what they're called. In the ring $\mathbb{Z}[x_i,y_i : i \in I]$ one has ...
0
votes
0answers
16 views

What's the difference between “is defined as” and “is described by the following axioms”?

I've often seen people saying that counting all the axioms for an object $x$ is not the same as defining it. How is it so?
1
vote
0answers
29 views

What is this notaton in Genus Theorem called?

Recently I started studying the book "Advanced Number Theory, by Harvey Cohn". Actually I know nothing about "Quadratic Forms". There I found this theorem: Let $$Q_1=x^2+5y^2$$ and ...
1
vote
2answers
93 views

Has this number triangle been studied?

Let's make a number triangle like this. $\sum 1 = x$ $ \sum \sum 1 = \sum x = 1/2 x + 1/2 x^2 $ $\sum \sum \sum 1 = \sum \sum x = \sum 1/2 x + 1/2 x^2 = 1/6 x^3 + 1/2 x^2 + 1/3 x $ ... So the ...
3
votes
1answer
32 views

Is there a name for those elements $x$ of a commutative ring $R$ such that $Rx$ is maximal among all proper ideals?

Ever since learning basic ring theory, I've always felt kind of confused about the fact that: maximal ideals are prime (because every field is an integral domain), but irreducible elements needn't ...
0
votes
2answers
43 views

Question about 'strong' assumptions and proving 'strong' result.

When someone says "we can prove a stronger result", it means the new statement is more general and better than the previous. However, when we add conditions to an argument, add more assumptions, we ...
0
votes
1answer
26 views

Do digits have a name based on position in a number, front or rear?

This is a question about terminology when dealing with numbers, counting and incrementing digits. In a decimal system we have 0-9 or 10 digits. Once we get past 9 we have to add a ? digit to get 10. ...
0
votes
0answers
21 views

Are these tree-related concepts redundant?

I've been doing a lot of work with trees lately, and have developed vocabulary that I've been using to describe them. Not having that strong of a background in graph theory, it occurred to me that I ...
0
votes
1answer
19 views

Measures which are constant when not zero

Let $S$ be a finite set. I want to consider measures $\mu$ on $S$ which are constant only when not zero. As an example, let $S$ be $\{a,b,c,d,e\}$, and take the measure: ...
0
votes
1answer
13 views

Connectivity with minimal width

Suppose you have a land-estate $L \subseteq \mathbb{R}^2$. You want to be able to drive in your car from each point in $L$ to each other point in $L$. The width of the car is $w$. So, it is not ...
3
votes
0answers
18 views

About Special and Extra-special $p$-groups

A $p$-group $G$ is said to be special $p$-group if $Z(G)=[G,G]=$ elementary abelian. A $p$-group $G$ is said to be extra-special if $Z(G)=[G,G]=$ elementary abelian of order $p$. The ...
4
votes
0answers
56 views

Are the terms 'clan' and 'tribe' common in mathematics?

In the book 'Vector Measures' by Dinculeanu, he starts the discussion by talking about "classes of sets", and introduces two pieces of terminology I've never seen before, and can't find any evidence ...
4
votes
0answers
32 views

What do you call two groups with only trivial homomorphisms between them?

Suppose $G$ and $H$ are groups, and all group homomorphisms $G \to H$ and $H \to G$ are trivial. Is there a common term to describe such a pair of groups with? Like, “$G$ and $H$ are [...]”, or “$G$ ...
3
votes
2answers
466 views

Why are contravariant functors called contravariant?

I'm just now learning a bit of category theory, and there often seems to be a certain notion, like limits for instance, and if you inverse certain arrows, you obtain a co-object related to that notion ...
1
vote
1answer
19 views

Term for using a number as an exponent (complementing “raise to the power of …”)

If we have an equation we want to solve such as $\sqrt{x} = 3$, we can say something such as square both sides or "raise both sides to the power of 2", to arrive at $x = 9$. So $3 \rightarrow 3^2$ ...
5
votes
2answers
73 views

Probability: mathematically what does it mean to say “let $X$ be a random variable WITH a cdf/pdf”

I don't quite understand what people mean by let "$X$ be a random variable WITH a cdf/pdf". For example, there is a question that says: "Let X be a random variable with the 3-parameter Weibull pdf and ...
2
votes
0answers
21 views

Are there generic terms or names to refer to elements of the domain, codomain, and range of a function?

Say I have a function $f:A\rightarrow B$. Is there some generic term or name for $x\in A$? (Something like "input" maybe? My goal is just to see if there's any standard term that's more succinct than ...
0
votes
0answers
5 views

Parallel series systems defined in OR? Isomorphism to SP-graphs in graph theory?

The series parallel graph definition is inductive with respect to series operation and parallel operation in graph theory. In comparison to series parallel systems in OR (Operations Research) and ...
0
votes
0answers
9 views

Inversely Proportional and Inversely Related

Suppose that we have a formula like $y=\frac{1}{\sqrt{x}}$. Is it correct to say that y is inversely proportional to x? what about y is inversely related to x? If not, what other phrase should we use? ...
0
votes
1answer
66 views

“This statement is false” - Propositional Logic

In a text I am reading, the section on Propositional Logic says that a proposition is a statement that is either true or false, but not both true and false. Also, from this lecture online, the ...
0
votes
1answer
29 views

Terminology re Bijection elements vs. Relation elements

Suppose I have bijection $X \rightarrow Y$. Is there a specific term for an element of $X$, which conveys the fact that the element can only map to one element of $Y$? E.g. "key" ? Now suppose I ...
28
votes
2answers
2k views

What comes after length, area and volume? [duplicate]

The length of the unit is 1. The area of the unit square is 1. The volume of the unit cube is 1. The $\color{red}{???}$ of the unit tesseract is 1. The $\color{blue}{???}$ of the unit ...
1
vote
3answers
165 views

“This statement is false.” [duplicate]

In propositional logic, a proposition is a statement that is either true or false, but not both. In a text I am reading and in many others, "this statement is false" is not considered a proposition. ...
0
votes
0answers
47 views

The expression “back to the envelope calculation”, what does it mean?

I'm french and one of my teacher use often the expression : "back to the envelope calculation", but I don't find any satisfactory translation. If someone know the french, and a good translation of ...
0
votes
2answers
35 views

Growth of debt: exponential, logarithmic, or linear? [closed]

If I have increasing debt that I don't intent to pay off for a really long time, how would I prefer to have it grow? Exponentially, logarithmically, or linearly?
1
vote
1answer
24 views

What is the difference between to “draw” and to “describe”

Reading the famous book "The Elements of Euclid". And I found this: Draw [a dotted line] (post. I.), describe [a triangle], and produce [another line]. In here, the word "Draw" and the word ...
0
votes
1answer
25 views

Meaning of denseness in a $L^p$ spaces?

I am currently studyind Density theorems in $L^p$ - spaces. In that, I have encountered a theorem which goes like this - The space of integrable simple functions is dense in $L^p $(E, $\mathcal{A}$ ...
1
vote
1answer
71 views

Does the function $f(x) = \frac{x}{|x|}$ have a name?

Does the function $$f(x) = \frac{x}{\operatorname |x\ |}$$ have a common name in mathematics?
3
votes
0answers
44 views

Does the function $\log(1+\exp(x))$ have a conventional name?

Does the function $\log(1+\exp(x))$ (or the function $\log(1+\exp(-x))$) have a conventional or at least fairly common name? Alternatively, is it closely related to some reasonably well-known, named ...
1
vote
2answers
31 views

Problem in understanding definition of absolutely continuous?

Suppose $(E, \mathcal{A})$ is a measurable space. Let $\mu$ and $\gamma$ be two distinct measures of this space. Now we say that $\gamma$ is absolutely continuous with respect to $\mu$ if for every $A ...