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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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What does it mean when a bound is sharp?

I've been reading this paper about the maximum size of digraphs. The author mentions that one of the digraph has a sharp bound. What does it mean when a bound is sharp?
Ong
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2 answers

Difference between a theorem and a law

There are plenty of theorems out there as well as laws within mathematics. For example, in Boolean algebra: Theorems Idempotent Involution Theorem of Complementarity Laws Commutative Associative Distributive There are countless other examples…
James Mertz
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what exactly is mathematical rigor?

I am a programmer moving up to computer science and even in my past life as a mechanical engineer I used sufficient maths to get by but I have always wondered what exactly is this thing called rigor. Please make me understand it.
shaw31
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What's the difference between list and sequence (as mathematical concepts not programming point of view)?

What distinguishes between set, multiset and list is whether the order is important or not, and whether repetitions of elements is allowed: List: order is important and repetition is allowed Multiset: order is not important but repetition is…
LoMaPh
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1 answer

"Total" degree of a polynomial?

What is the difference between the "degree" of a polynomial and its "total degree"?
MasterScrat
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If A = B, then B = A... Not Always True? Definition of "="

A friend and I recently got into a silly argument where I stated A = B so B = A. He stated this was not always true. After asking for an example he stated Jacuzzi = Hot Tub Hot Tub ≠ Jacuzzi Meaning all Jacuzzi's are hot tubs but not all Hot Tubs…
DoubleDouble
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10
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Why do we use open intervals in most proofs and definitions?

In my class we usually use intervals and balls in many proofs and definitions, but we almost never use closed intervals (for example, in Stokes Theorem, etc). On the other hand, many books use closed intervals. Why is this preference? What would…
jinawee
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9
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1 answer

Algebraic definition or construction of real numbers

Is there any algebraic definition or construction of real numbers ? If not, why ?
halfpog
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2 answers

Proper Use of the Term "Witness"

I was wondering what the term "witness" means in a mathematical context. I've heard and seen it used a bunch of times, but I'm still unsure of how/why the term is used or when to use it. Perhaps someone could give a few examples of when the term…
Simplicio
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8
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3 answers

What is the "Donkey Theorem"?

I was watching the Turkish version of Who Wants to Be a Millionaire? and they asked this question: What field is the Donkey Case (or I guess it can be translated as Donkey Theorem) related to? The correct answer was Mathematics. I've never heard…
Mehper C. Palavuzlar
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2 answers

Definition of notation $\mathbb Z_n$

What does the notation $\mathbb Z_n$ mean, where $n$ is also an integer. I have only seen $n$ being a positive integer up to now. some examples are $\mathbb Z_2$ or $\mathbb Z_3$ This is the context: How to prove $x^{2}+x=1$ has a solution in…
Asinomás
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6 answers

How to define relation of "bigger" and "less" and not run into a circularity?

Note: In the post by number I mean real number. What is a definition of the relations "bigger" and "less" ? The definition I saw in my book was "$a>b$ if $a-b$ is a positive number" and "$a
Юрій Ярош
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7
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1 answer

Define positions of a set of points given (only) the distances between them

I have been thinking about spatial transforms. Given $n$ points, there are $\frac{n!}{(n-2)!2!}$ combinations of selecting two points, so for 64 points in space, there are 2016 single point-to-point relationships (e.g. distances between points…
Andrewb
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The interest rate last year was 2%, this year it is 3% - did interest rates go up 1% or 50%

I've heard some experts say 1% and other experts say 50% to describe this same scenario. Can both be correct? Which one is more mathematically correct? How do you remove ambiguity when trying to describe this scenario?
Jeff
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Is there a definition for the"size" of a number?

To clarify my question, here is an example: We know that $1 < 2$ or $2 > 1$ (one is less than two, or, two is greater than one), but is this only based on our intuition or natural understanding of "size"? To ask it in a different way, what does it…
Sinos
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