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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1answer
81 views

Name of the matrix transform $AA^*$ given A?

There are a number of places this matrix transform making its appearance: Every positive semi-definite matrix $B$ can have a decomposition $B=AA^*$ If the matrix $A$ is a lower triangular matrix ...
0
votes
0answers
29 views

Is there a name for the subDAG of all the descendants (or ancestors) of a node in a DAG?

Is there a name for the subDAG of all the descendants (or ancestors) of a node in a DAG? DAG stands for Directed acyclic graph. A bibliographic pointer would be extremely helpful.
0
votes
0answers
39 views

Is there a name for an object with both position and velocity?

I know of "position vectors" and "velocity vectors". I'm looking for the name of an object which contains both a position vector and velocity vector, if such a name exists?
4
votes
4answers
578 views

How to formulate that an equation be shown to have no solutions?

Is there any general way to formulate the statement that an equation has no solution? For example: Prove that this equation has no solution: $$x^{1/\log x}=5$$ N.B. Do not answer with a ...
1
vote
1answer
29 views

Slice, projection, contour: A terminology question.

Consider a multivariate function, say $y=f(x_1,x_2,\dots,x_n)$, and suppose that $z=f(x_1,x_2,\dots,x_{n-1},g(x_1,x_2,\dots,x_{n-1}))$. What do we call $z$ with respect to $y$? Projection, level set, ...
1
vote
0answers
45 views

“Finite” includes Zero?

It is accepted that the empty set, of cardinality 0, is a finite set. So for phrases like "all but finitely many", or there is "a finite number of", is it accepted that they include the 0 ...
1
vote
0answers
21 views

Usage: Holomorphic Functions

This isn't a math question, but rather a question is word usage in mathematics. Why do people say " $f$ is an isomorphism," or "$f$ is a diffeomorphism," but in complex analysis, we say that "$f$ is ...
1
vote
1answer
21 views

Is there a name for the coordinate on a function which has maximum curvature?

I found out how to find the maximum curvature, by differentiating the curve function. I am wondering if there is a mathematical term, or if there isn't one what is the most elegant way to represent ...
19
votes
9answers
4k views

Is there a word similar to “iff” meaning “one and only one”?

I find the word "iff" for "if and only if" quite helpful for brief statements, but is there a similar one meaning "one and only one"? edit In light of the ambiguities some of the answers so far hint ...
0
votes
0answers
13 views

What is the classification for this dynamic model?

I have the following dynamical system \begin{align*} \dot x(t) &= f(x(t),y(t),t) + w(t)\\ 0 &= g(x(t),y(t),t) \end{align*} where $w(t)$ is zero-mean, white Gaussian noise process. I was ...
2
votes
1answer
54 views

What kind of cohomology is meant?

What kind of cohomology is meant in Deligne's work about mixed hodge structure on cohomology groups of an complex algebraic variety? I think it refers to the singular cohomology with coefficients in ...
0
votes
1answer
29 views

what does it mean to extrapolate?

Doing an assignment and got up to this question "Is is sensible to extrapolate the graph back to the moment when the population was zero? Explain" Don't know how to answer it because I do not know ...
0
votes
2answers
46 views

Names for complement of the union and intersection of two sets.

What is a good name for $ (A \cup B)^c $ or the complement of the union of two sets? Not union? NOR? Union complement? And what is a good name for $ (A \cap B)^c $ or the complement of the ...
0
votes
0answers
26 views

Translation of GENUS to Portuguese

Does somebody know a translation (to portuguese) for "genus" in topology? Theorem: A nonsigular projective curve in $\mathbb{P}_2$ is topologically a sphere with $g$ handles. Definition: This number ...
8
votes
6answers
978 views

what is this sort of function called?

I am doing an assignment but I do not know how to do this problem. I have the following: $$ f(x)= \begin{cases} 0 & \text{for $x<0$},\\ x & \text{for $x\geq 0$}. \end{cases} $$ We are ...
0
votes
0answers
21 views

Spelling: nonabelian or non-abelian?

This is not really a maths question, rather an English language question. Apologies if it's already been asked, it's hard to search. If I wanted to be scrupulous about correct spelling, is there any ...
3
votes
4answers
208 views

How should the term “stronger” be used? Example: groups stronger than semigroups or semigroups stronger than groups?

Everyone is well-known that every group is a semigroup. Then I should say that "group is stronger than semigroup" or "semigroup is stronger than group". Someone told me that stronger means more ...
3
votes
0answers
25 views

Center of the dual of a Lie algebra

Let $\mathfrak{g}$ be a Lie algebra. Let $C \subset \mathfrak{g}^*$ be the subspace of linear forms that vanish on Lie brackets: $$C = \{\alpha \in \mathfrak{g}^*, ~ [\mathfrak{g}, \mathfrak{g}] ...
0
votes
2answers
29 views

The conditions that partial derivatives commute

State the conditions that partial derivatives commute, namely, $D_1D_2f = D_2D_1f$. I understand how to prove that these partial derivatives are equal but I don't understand what commute means. ...
1
vote
0answers
46 views

What really is inductive reasoning?

I am looking for concrete information on "induction" in the old sense of the word. Now it is used to refer to proof by "mathematical induction"; however, I am aware that it also means inductive ...
1
vote
1answer
34 views

difference between equivalent and equal sign

I am reading a statement in which we have to show that $f(x)$ is equivalent to $0$ on an interval. What is differences $f(x)$ is $0$ and $f(x)$ is equivalently $0$ on an interval. Please help. ...
0
votes
0answers
34 views

Correct name for non-unit length 'hessian normal form' 3D plane.

A plane defined as 4 numbers (x,y,z,distance) is known as the hessian normal form, Where the xyz values are unit-length. However I've found its not necessary to ...
1
vote
2answers
38 views

What do you call the operator that takes in a number and spit out sets?

For example, I want to define an operator $P$ that takes in a value and gives all the partition of that value i.e. $P(3) = \{\{3\},\{2,1\},\{1,1,1\}\}$ What do I call such an "operator" $P$?
2
votes
0answers
43 views

a.s. for all $t$ or for all $t$ a.s.?

Assume that we have some equality, $$ X (t) = Y(t). \quad \quad \quad \quad \quad \quad \quad (1) $$ I imagine that if I say "(1) holds a.s. for all $t>0$" it means that $$ P\{X (t) = Y(t) ...
0
votes
3answers
45 views

What is an nonlinear ordinary differential equation and give an example?

What is an nonlinear ordinary differential equation and give an example? And what is the difference between an linear ordinary differential equation and non-linear ordinary differential equation in ...
5
votes
4answers
117 views

Term for similarity transformation which is not a translation

What's the best (i.e. most concise) term to refer to an orientation-preserving similarity transformation which is not a translation? Here are some descriptions I could think of, but all of them feel ...
1
vote
0answers
42 views

Can $y = x^\sqrt{3}$ be considered a Power function? What about a polynomial?

Can $$y = x^\sqrt{3}$$ be considered a Power function? What about a polynomial? Also, is $$y = \sqrt{3}^x$$ an exponential? I am curious about the boundaries which define each type of function. ...
0
votes
1answer
11 views

What exactly does it mean that the key $e \in \mathcal K$ uniquely determines $E_e$?

What exactly does it mean that the key $e \in \mathcal K$ uniquely determines $E_e$ ? Does it mean that for each $e \in \mathcal K$ there exist only one function $E_e$ corresponding to $e$ ? Does ...
0
votes
1answer
61 views

Number theory used in cryptography [duplicate]

I am entering the realm of cryptography and encountering Number Theory related stuff a lot (As expected). I have a good knowledge and background on mathematics but I have been away for a while. So if ...
2
votes
1answer
70 views

Definition of “descends to”

My textbook keeps saying that maps "descend to" other maps. I have never encountered this terminology before (at least not in English). What does it mean? Here is an example: The function $H$ is ...
1
vote
1answer
38 views

What is isobaric function?

I'm reading My Numbers, My Friends by Paulo Ribenboim and I've encountered this: Thus $U_n = f_n(P,Q)$, where $f_n(X,Y) \in \mathbb{Z}[X, Y]$. The function $f_n$ is isobaric of weight $n-1$, where ...
3
votes
0answers
94 views

Cell theory - What is it? - Reference request

A user with $>10,000$ posts on sci.math called 'plutonium.archimedes' or 'AP' is constantly ranting about some theory he deems superior to calculus(a.k.a 'old math' I believe). I can't find any ...
1
vote
1answer
25 views

Local homeomorphisms: terminology

Let $(E,\pi,X)$ be a local homeomorphism, so for any $x\in E$ there is an open set $U\ni x$ such that $\pi|U$ maps $U$ homeomorphically onto $\pi[U]\subseteq X$, and $\pi[U]$ is open in $X$. Is there ...
0
votes
2answers
18 views

Name for line segment parallel to triangle base

In describing an elegant construction of a regular pentagon, i'm struggling to find a nice way of describing the following: A line segment starting at a point partway up one side of a (in this case, ...
1
vote
1answer
26 views

Clarification on rings of polynomials / Galois fields

I need some clarification about what the following thing is called (it's commonly used to describe linear-feedback shift registers), and what a good computer program identifier would be that describes ...
1
vote
1answer
48 views

“Octahedron” made from two pyramids of different heights.

I wonder how to name such shape: It's commonly used by e.g. 3ds max to visualize the bone in animation system. It consist of two pyramids with the exact same square base. It would be a ...
2
votes
1answer
16 views

Terminology - Union of kernels of iterated linear functions

Quick question: if $V$ is a $K$-vector space, $f : V \to V$ a linear function and $f^k = f \circ \ldots \circ f$ ($k$ times), does $\mathscr U = \displaystyle \bigcup_{k\ge 1} \ker f^k$ have ...
4
votes
2answers
142 views

The meaning of Sprague-Grundy ordinal

I have an unusual request to you. I speak English badly (I'm from Russia). Май инглиш из вери бед (sorry, Russian stupid joke). I'm writing a term paper. I faced with the problem of translation of ...
1
vote
3answers
44 views

What does is mean for a transformation to preserve an operation?

I read this sentence in Linear Algebra and its Applications: "Linear transformations preserve the operations of vector addition and scalar multiplication," but I don't know preserve means in this ...
0
votes
0answers
11 views

component-wise independent vector field

Suppose you have an $n$-dimensional vector field defined by $$ \mathbf{F}(\vec{x}) = \langle f_1(\vec{x}),...,f_n(\vec{x})\rangle $$ I would like to know what it is called when the $i$'th component ...
4
votes
6answers
372 views

In what sense of “structure” do group homomorphisms “preserve structure”?

It is commonly said that group homomorphisms "preserve the structure of the group", e.g., from Wikipedia: The purpose of defining a group homomorphism as it is, is to create functions that ...
2
votes
0answers
92 views

What is the name of proofs with (without) Axiom of Choice

In many contexts we distinguish between proofs using AC and proofs which do not use AC. (To phrase this somewhat differently: If there is a proof without AC, this proof is usually preferred.) I would ...
10
votes
3answers
3k views

What is the meaning of the expression Q.E.D.? Is it similar to ■ appearing at the end of a theorem?

I am curious about the meaning of the word Q.E.D. that is often written after a proof of a theorem (some math books use this convention). Edit: Is it similar to the box being placed after a proof of ...
0
votes
1answer
39 views

What is this statement mean “It is connected but not path-connected.”

What is this statement mean "It is connected but not path-connected." For example. topologist's sine curve is one of the example.
1
vote
1answer
32 views

What do we call the construction of a one object $n+1$-category (etc.) from multiobject $n$-category (etc.)?

In general, when we have an $n$-something ($n$-category, etc.) and we decide to push everything up a notch, so $n$-cells become $n+1$-cells, and we end up with a $1$-object $n+1$-something, what do we ...
-3
votes
1answer
62 views

what do these complex analysis terms mean?

I'd like to know the definition of the following terms I'm not familiar with... and to know if my understanding is misguided or in the right direction. In the brackets is what I believe it to be - ...
1
vote
2answers
66 views

Is definable $\emptyset$-definable?

A set $A$ is $X$-definable in an $L$-structure $\mathcal{M}$ with a domain $M$ iff there are an $L$ formula $\phi(a,\bar x)$ and $\bar x \in X^n$ such that $A=\{a \in M^m | \mathcal{M} \models ...
0
votes
1answer
37 views

Name of the difference between an asymptote and the curve that approaches it

Consider a function, say a hyperbola, and its asymptote. Is there a specific term for the difference between the two? Answers specific to hyperbola, as well as answers about general terminology, are ...
4
votes
3answers
431 views

What is this property called for a function? $f(f(x))=f(x)$

I am looking for a name for the following types of functions. Suppose that for function f, we have: $$f(x)=y_x$$ and $$f(f(x))=y_x$$ Is there any name for this property?
1
vote
1answer
33 views

The name for numbers with a certain digit sum.

What is the term for a number that has a certain digit sum? For instance 12 is the "digit sum" of 84, 138, 525 and so on. But what kind of number is 84, 138 and 525 to the number 12? Is there a term ...