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

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0
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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
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3answers
936 views

Orbit vs. Cycle

Can someone explain to me the difference between an orbit and a cycle?
6
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2answers
381 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. ...
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4answers
463 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
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2answers
712 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
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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
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2answers
786 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
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1answer
979 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
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1answer
717 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
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2answers
275 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
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1answer
177 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
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1answer
396 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
641 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
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1answer
2k 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
381 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
401 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
931 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.
23
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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
105 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
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2answers
445 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
450 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
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1answer
535 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 ...
1
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3answers
191 views

Are these statements about even numbers called symmetrical statements?

I have these following statements. x is a even number $\Rightarrow$ xy is a even number y is a even number $\Rightarrow$ xy is a even number Can I call them symmetrical statements?
11
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3answers
1k views

Meaning/Justification for Describing Functions as 'Orthogonal'

When introducing Fourier series, my lecturer stated that 2 periodic functions, $f$ and $g$, with period $2L$ are orthogonal iff $$\int^{L}_{-L}{f(x)g(x)}\mathrm dx=0$$ Wikipedia agrees, even defining ...
2
votes
2answers
1k views

What does a condition being sufficient as well as necessary indicates?

I have a question in a book I am solving(Discrete Structures by Kolman, Busby & Ross). I am unable to make sense from the question. It is stated below, Show that k is odd is a necessary and ...
11
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7answers
23k views

What is the difference between only if and iff?

I have read this question. I am now stuck with the difference between "if and only if" and "only if". Please help me out. Thanks
13
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3answers
3k views

Embedding, immersion

Could someone please explain what "embedding" means? (Maybe a more intuitive definition) I read that the Klein bottle and real projective plane cannot be embedded in ${\mathbb R}^3$ but is embedded in ...
8
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3answers
3k views

Proposition vs Theorem

What is the distinction between a proposition and a theorem? How do people decide which of the 2 to use in, say, textbooks? Somehow I think proposition sounds less serious... Thanks.
1
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0answers
59 views

Term for generalized antisymmetry?

As I understand it, a binary relation $R$ over a set $A$ is antisymmetric if for all $a, b \in A: aRb \land bRa$ implies $a = b$. Now, suppose that I have an equivalence relation $E$ over the set ...
3
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0answers
247 views

What's the origin of the terminology “Normalization” in commutative algebra?

Since the terminology "normal", "normalized", etc has different meanings in mathematics (some geometric in flavor, like when referring to perpendicularity) and I just read in Eisenbud's book on ...
9
votes
3answers
886 views

What does it mean to “count (some number) of (some finite set of objects)”?

I'm not a native speaker of English. I usually pride myself of my proficiency, but I think I may be stumped here. My problem arises out of this question, which among other things asked for a ...
20
votes
3answers
711 views

How to answer a student objection to the use of “of” in pronouncing f(x)?

Once upon a time in elementary school, a student learned how to translate certain English words into math. For example, 'and' usually means 'plus' such as "If John has 3 oranges AND 5 apples, how ...
0
votes
1answer
461 views

Positive semidefinite vector $\bar{x}$ as $\bar{x}>0 :=\bar{x} \lambda \bar{x}^{T}>0$?

$A \lambda A^{T} $ (quadratic form?) is used with matrices to check definiteness. What about with vectors? If I see conditions such as $\bar{x} > 0$, how can I know whether it means $\bar{x}_{i} ...
2
votes
0answers
268 views

Monodromy theorem in Princeton lectures in analysis

I am very curious to know if what is called the "Monodromy Theorem" or "Riemann Monodromy Theorem" is also known by some other name. For all my complex analysis requirements I have always fallen ...
1
vote
1answer
139 views

What is the name of this function on a graph?

I would like to know how this function is named to find how to calculate it. I have a trend like this one and want to find the upper and lower lines, the red ones (as you can see I do not have a great ...
3
votes
1answer
863 views

What is a cardinal basis spline?

Wikipedia says: the normalized cardinal B-splines tend to the Gaussian function and writes them as "Bk". Meanwhile, cnx.org Signal Reconstruction says: The basis splines Bn are shown ... ...
1
vote
1answer
106 views

Is the term Gaussian distribution the preferred term?

Is "Gaussian" the term preferred over "normal" when speaking of the distribution to which these names have been attached? Are they both referring to the same thing?
1
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2answers
138 views

How is that three-place logic operator called?

In the sources of Haskell's AwesomePrelude there is a 'bool' function with which all other operators can be defined (provided true and false are given): ...
5
votes
0answers
221 views

Does this property of scattered spaces have a name?

Let $K$ be a (Hausdorff) scattered topological space and for each ordinal $\alpha$ denote by $K^{(\alpha)}$ the $\alpha$th derivative of $K$ by the Cantor-Bendixson derivation (i.e., define ...
1
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2answers
2k views

Interpolation, Extrapolation and Approximations rigorously

A foreign book mentioned that "when the Lagrange's interpolation formula fails (for example with large sample due to Runge's phenomenon), you should use approximation methods such as ...
8
votes
2answers
376 views

What is the motivation for defining both homogeneous and inhomogeneous cochains?

In my few months of studying group cohomology, I've seen two "standard" complexes that are introduced: We let $X_r$ be the free $\mathbb{Z}[G]$-module on $G^r$ (so, it has as a $\mathbb{Z}[G]$-basis ...
4
votes
1answer
126 views

“belongs to” versus “contained in”

Let us consider a set $A$. let $B$ be an element of the set. Now what I want to know is that whether saying $B$ is contained in $A$ and $B$ belongs to $A$ means the same? Could anyone here cite any ...
2
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2answers
176 views

Is there a name for a non-iso monomorphism?

I am really bummed out to find that the term "strict monomorphism" is already used to mean something else. Can anybody console me with the knowledge that there is another name I can use for a ...
2
votes
0answers
73 views

Name for a Partition in which Every Block Has the Same Size

Is there a standard name for a partition of a set in which every block (i.e. the subsets comprising the partition) has the same size? Regular? Uniform? Something else? Nothing else (so I'm free to ...
1
vote
0answers
119 views

What is this called? [duplicate]

Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? I am looking for the name of an operation similar to factorial. Factorial would ...
18
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2answers
1k views

Once and for all - “Rational numbers” - because of ratio, or because they make sense?

This is a question I'm sure was asked before but I can't find it. There are many sources claiming that the term "rational number" for the elements of $\mathbb{Q}$ comes from the word "ratio", since a ...