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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2answers
382 views

Why was the term “integral” used to represent the area under a curve?

I have a colleague in the English dept. who is wondering the reason why the word "integral" came to be used to represent the process by which the area under a curve can be found.
0
votes
1answer
212 views

What does RMSD mean?

Normally a rigid superposition which minimizes the RMSD is performed, and this minimum is returned. Given two sets of points and , the RMSD is defined as follows: $$\begin{align*} \mathrm{RMSD}(\...
0
votes
1answer
78 views

What does $f$ is measurable as a function $f^{-1}(\mathbb{R})\to\mathbb{R}$ mean?

I saw a question where we have $\overline{\mathbb{R}}:=\mathbb{R}\cup\{\pm\infty\}$ and $(X,S)$ is a measurable space, $f:\, X\to\overline{\mathbb{R}}$ In one part I was told to assume that $f$ is ...
5
votes
0answers
548 views

When are two objects essentially the same?

From the comments to this question I have learned, that many (most?) mathematicians are not very interested in the relationship between an object $X$ and its "correspondent" $F(X)$ for an arbitrary (...
2
votes
1answer
104 views

Name of corresponding objects in equivalent categories

This question is only about terminology. Inside a category we have the standard wordings: An arrow $f: X \rightarrow Y$ is an isomorphism if there is another arrow $g: Y \rightarrow X$ such that $g \...
16
votes
2answers
12k views

What is the difference between kernel and null space?

What is the difference, if any, between kernel and null space? I previously understood the kernel to be of a linear map and the null space to be of a matrix: i.e., for any linear map $f : V \to W$, $...
2
votes
1answer
447 views

Injective Morphisms, Monomorphisms and Left Invertible Morphisms in Abelian Categories

Let $\mathcal{C}$ be an abelian category. A morphism $f:X \rightarrow Y$ is called injective if its kernel is zero. $f$ is called monomorphism if whenever $f \circ g=0$, for $g:Z \rightarrow X$, then $...
19
votes
4answers
312 views

Is there a name for this kind of “betweenness structure”?

A homeomorphism $\mathbb R\to\mathbb R$ is almost the same thing as an order isomorphism, except that a homeophorphism can also be an order anti-isomorphism. I'm wondering whether there is a natural ...
2
votes
2answers
4k views

How do I read this distribution function: $\min(X,Y)$?

I'm confused on what the $\min$ means. For example if I need to find the distribution function of $\min(X,Y)$ what am I looking for exactly? Am I looking for the distribution of the minimum value of ...
4
votes
3answers
228 views

Is there such a thing as function decomposability?

I am not a mathematician, so what I ask might be trivial, however I couldn't find something relevant in the web. My question is the following: Is there a formal notation for functions that comply the ...
0
votes
1answer
171 views

Correct reading of Set builder Notation?

could anyone please let me know the correct reading(sentence form) of set builder notation, confused with different interpretation in different resources. Many Thanks
3
votes
3answers
5k views

meaning of 'Hypothesis' in simple terms?

could anyone please clarify me the meaning of the term 'hypothesis'? with relation to terms 'reasoning' and 'assumption' ? Many thanks
1
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0answers
40 views

Correct term for trivial extension of linear operator on Hilbert spaces

Suppose we are given Hilbert spaces $Z = X \oplus Y$ and $C = A \oplus B$. Let $T : X \rightarrow A$ be a bounded linear operator. We can identify it with the operator $S : Z \rightarrow C$ that maps ...
1
vote
2answers
163 views

what does it mean to say a space is norm separable?

I came across in my textbook the term: norm separable. I looked in the textbook and online and could not find a definition.
1
vote
4answers
227 views

What do you call $-f(x)$

I have a terminology question. I am referring to a sigmoid (S-shape function) in a paper however it is inverted (if the sigmoid is $f(x)$, my function $-f(x)$). I initially wanted to refer to it as ...
0
votes
1answer
60 views

preserves eigen spaces?

"Let $H_0=\begin{pmatrix}i&0\\0&-i\end{pmatrix}$, suppose $A\in SU(2)$ commutes with $H_0$, it must preserves each eigen spaces for $H_0$, eigen spaces for $H_0$ are just $\mathbb{C}e_1$ and $\...
1
vote
2answers
68 views

Is the word “adjacent” being used correctly in this geometry problem?

I am trying to say Construct $\triangle ABC$ such that the extension of side CB is adjacent to side AB I am trying to avoid using poor ambiguous vocabularies like "to the right of AB"
1
vote
2answers
92 views

Geometry vocabulary.

Does anyone know how i can describe the point "x" that's in the picture? my best attempt so far is to say The point X is on the extended line segment of DE and lies outside $\triangle ABC$ and is ...
0
votes
1answer
579 views

What does it mean for a set to be “nested”?

What does it mean for a set to be "nested"? and can you please show an example of that is and one that isn't
1
vote
1answer
51 views

What is a memoryless nonlinear boolean function?

I have been reading about shift register based keystream generators in cryptography. One usual method of generating keystream sequences is feeding the output of several Linear Feedback Shift Registers ...
1
vote
1answer
224 views

Name for the real numbers between $0$ and $1$

I see this class of numbers all the time, so I was wondering if there was a special name for it. How to refer to a number $n$ in $\Bbb R$, such that $0<n<1$?
0
votes
2answers
188 views

Weak Partial Complete Lattice and Homomorphisms

What is the proper nomenclature for a generalization of a lattice $L$ such that not all subsets of $L$ may have a join/meet, sometimes not even for finite subsets? This paper calls it a "weak partial ...
4
votes
2answers
250 views

What is the word for a corollary that follows from a proof?

I know there's a particular word but can not think of it and have been unsuccessful finding it by googling. I want to say "porium" but that doesn't come up when I google.
2
votes
1answer
126 views

What does 'the forward theorem' refer to?

I have seen the following in a circle geometry proof in a Cambridge textbook: We have proven that angles at the circumference standing on the same arc of a circle are equal. The converse of this ...
2
votes
3answers
2k views

Is there a special name for the operands of a multiplication?

Sometimes operands for a specific operation are given a special name. For example, in division the first operand is a quotient, the second is a divisor. Is there a word that means "one of the operands ...
1
vote
1answer
496 views

Is there a name for position and dimension in the mathematics

I'm a Software Architect who looking for a corresponding term for position and dimensions of an object at the sametime. Is there a word or term for that in geometry or analytic geometry?
1
vote
1answer
141 views

What are the transformations of the plane called whose derivatives at each point are isometries?

Let $f:\Bbb R^2\to\Bbb R^2$ be a differentiable function. Are there names for the following two conditions? $Df(p)$ is an isometry at each point $p\in\Bbb R^2$; $Df(p)$ is a similarity at each point ...
8
votes
1answer
1k views

On 'backslash-forward slash' notation

I am curious about a notation that I have seen, but I have only seen it in contexts beyond my current level of ability and so haven't learned its meaning. Also, it's often difficult to search for the ...
11
votes
3answers
307 views

Is there a name for this ring-like object?

Let $S$ be an abelian group under an operation denoted by $+$. Suppose further that $S$ is closed under a commutative, associative law of multiplication denoted by $\cdot$. Say that $\cdot$ ...
4
votes
2answers
4k views

Name for diagonals of a matrix

I am looking for the terms to use for particular types of diagonals in two dimensional matrices. I have heard the longest diagonal, from top-left element and in the direction down-right often called ...
2
votes
3answers
2k views

Meaning of counting argument?

Does "counting argument" mean a proof of some statements by counting something? Is "counting argument" same as "double counting"? Or does it include both double counting and bijective proof? I ...
1
vote
2answers
105 views

Translation help needed about terminology in optimization from Finnish to English

I am studying the course Mat-2.3139 in Aalto University and I need to find translations from Finnish to English for a few terms. Some of my teachers claim that they are missing funding for ...
1
vote
0answers
34 views

Terminology: a notion of a set of “chords” for arbitrary subgraphs

I'm considering a problem on random graphs, where it makes sense to look the edges which "touch" a connected component, but which do not belong to it. Consider a fixed graph $G$, where as usual we ...
3
votes
1answer
871 views

Are “deterministic” and “idempotent” just two different names of the same concept? [closed]

Sometimes I encounter the term "deterministic" and sometimes I encounter "idempotent" in describing functions . Are they just ...
2
votes
0answers
48 views

Terminology: is there a term for one order being on a geodesic between two others in the Cayley graph?

Think about the graph whose nodes are total orders on a finite set, and whose edges connect orders that only differ on two elements. This is actually a Cayley graph of $S_n$, but I don't want to fix ...
2
votes
2answers
69 views

Is there a name for the set $\{T,F\}$?

Is there a name for the set containing the two Boolean values, i.e. $\{T,F\}$? I am also thinking if $B = \{T,F\}$, and $B^n = \underbrace{B \times B\times B ... \times B}_n$, then is there a proper ...
3
votes
3answers
276 views

Naming quadrilaterals

Is there a rule for naming quadrilaterals in English? What I am expected to know about are: square, rhombus, rectangle, parallelogram, trapezium, kite. But how do we name other quadrilaterals?
1
vote
1answer
187 views

Riesz, Hilbert and Hamel bases

I was surprised to read both at PlanetMath and in Wikipedia (apparently copied from PlanetMath) that If $H$ is a finite-dimensional [Hilbert] space, then every basis of $H$ is a Riesz basis. I ...
5
votes
1answer
105 views

What do you call a function differentiated with respect to all of its arguments?

Just a simple question. Let $f(x_1, x_2, \ldots, x_n)$ be a smooth function. Is there a particular name for the function $$\frac{\partial^n f}{\partial x_1 \, \partial x_2 \cdots \partial x_n}$$
0
votes
2answers
277 views

What does integrating a function $f(x)$ with respect to a function $g(x)$?

I encountered the following question in my book: "Integrate $f(x)=\sqrt{1+x^2}$ with respect to $x^2$." I am a bit confused about what this is supposed to mean. In general, what does it mean to ...
0
votes
1answer
451 views

definition from mathematics translated in english language

guys this question is more specific related to english and math together then math only,i am studying GRE tasks(quantity variant) and want to be acquainted every term and trick related to ...
11
votes
2answers
223 views

What is the gender of $K(\pi,n)$ in French?

This is a kind of silly question, but I don't know where else to ask. Suppose I wanted to say "Ceci n'est pas une pipe" but with $K(\pi,n)$ substituted for "pipe." Would the article be "un" or "une"? ...
1
vote
0answers
135 views

Etymology of algebra (as k-algebra)?

Why algebra (over a field) is called "algebra?" (My random guess is that it's a back-formation of some algebras, chopping adjectives from say Lie algebra or Clifford algebra, etc.) And when was that ...
1
vote
1answer
126 views

How do you say “function with fewer oscillations?”

Say you have a few functions on the same graph that oscillate, but they're not sine functions, they're polynomials. (These are Legendre polynomials) How do you refer to the "curvier" ones without ...
0
votes
2answers
143 views

Confusion over the usage of different terms for ref and rref.

My school uses row echelon form and reduced row echelon form to denote their respective types of matrices which results from gauss jordan elimination. Today I came across this term used in this ...
3
votes
1answer
156 views

What does arithmetic actually mean (as an adjective)

Ok so I've seen the adjective 'arithmetic' (stress on the e) bandied about from time to time in reference to the "arithmetic theory of some subject" (elliptic curves for instance), or the "arithmetic ...
0
votes
0answers
143 views

What is the correct definition for an imaginary number? [duplicate]

The following is taken from Wikipedia's definition. An imaginary number is a number whose square is less than or equal to zero. But I also heard that An imaginary number is a number whose ...
6
votes
1answer
451 views

Name of a set that allows repetition

If a set cannot contain repetition, what would be the proper term for a group of items that allowed repetition?
1
vote
1answer
227 views

Sufficient/necessary vs. weaker stronger

I know what sufficient resp. necessary means, but I'm confused, when our professor uses the terminology weaker resp. stronger. I couldn't yet find out, what the translation of these pair of words to ...
8
votes
3answers
8k views

Difference between “intercept” and “intersect”

What is the difference between intercept and intersect? Can they be used interchangeably? For example, intersecting lines and intercepting lines.