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Questions tagged [definition]

For requesting, clarifying, and comparing definitions of mathematical terms.

Definitions are at the core of mathematical precision; they answer the question "What is X?" in mathematics. Into this category fit questions regarding equivalence of definitions, clarification of complicated definitions, or proposed new definitions for mathematical notions, with requests for improvements or comments.

7799 questions
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Why are the summands $-1,0,1$?

I have some problem to understand the following: Let $X=\left\{0,1,2\right\}$ and consider $X^{\mathbb{Z}^d}, d\geq 2$ as being the set of all function from $Z^d$ to $X$. So for $\eta\in X^{\mathbb{Z}^d}$ it is either $\eta(x_i)=0$, $\eta(x_i)=1$ or…
user34632
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What is the word for the numerical portion of a numeric value with units?

When I see 3 Miles the word "miles" represents the units. What is the word which 3 represents? I want to say "scalar value" but I know that's not correct. Or if it is correct is 4 also the scalar value in the phrase "4 square miles"? Is the word…
Corey Alix
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Is a definition either intensional or extensional?

Is a definition either intensional or extensional? Can a definition be neither? Can a definition be both? How about this definition? when there is only one object that satisfies a definition, e.g. define $A:= 1$ I think this definition of $A$ is…
Tim
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Writing order of geospacial coordinates

Is there a defined order in which to write geospacial coordinates? When looking at GPX files generated by my GPS, latitude is named first but when looking at a KML file generated by google earth longitude is first. I tend to think of longitude as…
DudeOnRock
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What does $\text{mod}\ m$ in $a \equiv b (\text{mod}\ m)$ means

I am trying to do example 3.6 from this http://www.cs.fsu.edu/~lacher/courses/MAD3105/lectures/s1_3equivrel.pdf script, but I am not sure what does $(\text{mod}\ m)$ means. Can somebody explain it to me. Thanks.
depecheSoul
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Definition convex sets

$C$ is convex $\Longrightarrow \forall x,y \in C$ and $\forall$ $t\in [0,1], \space(1 − t ) x + t y \in C$ My question how comes this formula $(1 − t ) x + t y$ describes all the elements in $[x,y]$ with $t\in [0,1]$?
mohamez
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What is the meaning of | operator?

For example, 12|0 = 0 Interesting I can't find this on google anywhere. Which logical connective is this? as in this article http://www.mathblog.dk/strong-induction/
Thomas
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What is a "lemma"?

As per title, what is a "lemma"? How is it different from "theorem"? ASAIK, I have to prove a self-proposed theorem in my paper. Do I also have to provide the proof for a self-proposed lemma?
Sibbs Gambling
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Question about theorem involving GCDs?

From http://www.math.niu.edu/~beachy/abstract_algebra/study_guide/11.html, it says Theorem 1.1.4. Let I be a nonempty set of integers that is closed under addition and subtraction. Then I either consists of zero alone or else contains a smallest…
Don Larynx
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Is there a standard definition of what it means for points to be uniformly distributed?

I'm working on something where it is important that some points are "uniformly distributed" over the unit square. Here's a somewhat simplified version of what I'm working with: Let's say that for each natural number $n$ we have a set of points in…
Polygon
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Conflict between mathematics and physics regarding a constant signal

In mathematics, we learned that a constant function is periodic but does not have a smallest positive period (fundamental period). Consequently, I conclude that a constant signal has no frequency. However, in physics, we learn that a constant…
Ziad
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How to evaluate this "summation style" integral produced by Wolfram Alpha?

Let $f(x,y)=xy/(x+y)$, Let $\phi$ be a formal variable, and define a sequence $\lambda_n$ as follows: $$\lambda_1=\phi^2+\phi^1$$ $$\lambda_2 = f(\phi^4 + \phi^3, \phi^2) + \phi^1$$ $$\lambda_3 = f(f(\phi^6+\phi^5, \phi^4) + \phi^3, \phi^2) +…
Snared
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Defining the global maxima for an $L^2$ function

I am writing the definition of the global maxima of the square of the absolute value of an $L^2$ function, which looks like this: Here the global maxima is at $x=0$. So I want to make the definition of this global maxima, and I define it as…
Luthier415Hz
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Is the Fibonacci spiral a "proper" spiral?

I'm not a mathematician. Merriam-Webster defines a spiral as "the path of a point in a plane moving around a central point while continuously receding from or approaching it." Other sources I checked don't mention the word "continuously". MathWorld…
stevenvh
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Is this mapping considered bijective?

I am not fluent in MathJax nor math lingo, so please bear with me. As I understand, for these declarations (consider these sets as ordered): $L=\{a, b, c\}, l \in L$ $N=\{1, 2, 3\}, n \in N$ the following mapping is considered bijective, as it's…
Cromax
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