Mathematics Stack Exchange
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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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Is $2+2=4$ an identity?

I know this seems like a silly question, but someone was trying to debate with me about how $2+2=4$ should be called an identity and not an equation. I mentioned how it has no variables and isn't true for all numbers, but they claimed you could plug…
Lee
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Why is a 4th root always positive?

I am now teaching mathematics and in the math book for the students, it says that a 4th root is always positive. I have never thought about this rule before but actually, say for example: $\sqrt[4]{16} = 2 $ because $ 2^2=4$. But also $(-2)^4 =…
Mr. P
  • 175
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What is the differentiation operator

On Wikipedia the Differential Operator is described as an operator defined as a function of the differentiation operator. The link that underlies the words "differentiation operator" in fact gives many different concepts related to differentiation,…
harlekin
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Are the words "function", "map", and "mapping" synonymous?

Is it correct to say that "A function or a map or a mapping is a binary relation such that ..."
user46234
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1 answer

What is the definition of "formal identity"?

In Ahlfors' Complex Analysis he remarks that harmonic $u(x,y)$ can be expressed as $$ u(x,y) = \frac{1}{2}[f(x + i y) + \overline{f}(x - i y)] $$ when $x$ and $y$ are real. He then writes "It is reasonable to expect that this is a formal identity, …
bryanj
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What does $\mathbb Z_+$ mean?

I am not so sure whether the meaning of $$\mathbb Z_+$$ is very clear. How many different definitions are there? Does the definition that is used depend on whether the writer is English or German? In French maths, this notation doesn't exist.
Damien L
  • 6,649
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What is a variable as opposed to a parameter?

What is a variable as opposed to a parameter? I have never seen or heard of a clean definition. As of my opinion, a parameter is a fixed value, whereas a variable is, deep thought, the result of an undefined function, like it is for "stochastic"…
Gyro Gearloose
  • 1,142
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What does "within $x$% of $y$" mean?

I cannot find a specific definition for "within $x$% of $y$". If I want a number within $10$% of $100$, am I looking for numbers in the set $[90,110]$? Or does it mean percentage difference? Or percentage change?
Lucas Alanis
  • 1,406
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Definition of global field

This is very embarrassing thing to ask but what is a definition of global field? Every text or internet sources says either a number field or function field over finite field. (Yes, I understand there is nothing wrong with this but I would like to…
Jack Yoon
  • 1,466
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How to define the disciplines of mathematics

Would you say that it is possible to give a unified, general definition of the different structures of mathematics and draw a clear distinction between them? I have been repeatedly trying to come up with such a distinction myself, but they either…
Gaussler
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Definition of a sphere

If there is no further specification (such as solid or hollow), does a "sphere" refer to the solid/filled form or the hollow shell? Thanks.
sphere
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Is there a specification language that covers all of these classes of structures?

Classes of mathematical structures abound in modern math. Examples include: The class of all groups. The class of all partially-ordered sets. The class of vector spaces. The class of ordered fields isomorphic to $\mathbb{R}$. The class of all…
goblin GONE
  • 67,744
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What is the mathematical definition of index set?

I find some descriptions http://en.wikipedia.org/wiki/Index_set and http://mathworld.wolfram.com/IndexSet.html . But can't find any definition.
RHS
  • 413
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What does it mean for a set to be bounded?

I've been trying to prove a slightly different statement to the definition of the well ordering principle given by Lang in Undergraduate Algebra and given here for reference: Every non-empty set of integers $\geq 0$ has a least element. I've been…
user70962
4
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2 answers

Definition of kernel

Is the kernel the same as the union of all level sets (or perhaps the set of all level sets)? Kernel (https://en.m.wikipedia.org/wiki/Kernel_(set_theory)): $\left\{\, \left\{\, w \in X \mid f(x)=f(w) \,\right\} \mid x \in X \,\right\}$ Level set…
Emil
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