Mathematics Stack Exchange
Mathematics Stack Exchange

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 is it called when a decimal value has a pattern while infinite?

I recently made an edit to this post concerning $\pi$ and it containing all possible combinations of numerical values; and this answer to it brought forward an interesting number: 0.011000111100000111111… This got me thinking; what is it called…
Hazel へいぜる
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Definition of "definition": use iff or if?

There are topics with the same name but my question is not as abstract as in those. My question is as follows: taken a generic definition like $x\;\mathbf{ is\; something}$ if $y$ it could be written like $x\;\mathbf{ is\; something}\Leftarrow y$ so…
Mega-X
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Trying to understand an abstract definition of power series..

Can anyone explain to me what the $X_{n}$ and $X_{n}^{m}$ are really standing for? Starting from "We write X for the power series..."
pigeon
  • 161
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When does a digraph have infinite radius?

For a graph with infinite radius, the graph is disconnected. When does a digraph have infinite radius? Is it possible for a connected digraph to have infinite radius?
Ong
  • 233
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Why is there no equivalence in the definition of injection?

Everywhere I found that the definition of an injection only uses an implication. However, I can't think a case where if $f$ is an injective function, and if $a = b$, then $f(a) \neq f(b)$. Why do we use an implication ?
ChatPion
  • 21
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May I use comma to avoid redundancy in expressions?

Is it generally possible to write $$1\leq k,l\leq 8$$ instead of $$1\leq k\leq8\quad \mathrm{and} \quad 1\leq l\leq 8$$ to avoid redundancy?
Daniel Langr
  • 227
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Is everything an expression?

Is everything that you can write in math (that makes mathematical sense) an expression? If not, what would be examples of non-expressions? And would all expressions be composed of expressions themselves? Also, are operators (like the differential…
wrongusername
  • 1,309
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What is $L_{loc}^1$

What is $L_{loc}^1$? I know what $L^1$ is. I saw this on page 15 in the book Variational Analysis in Sobolev and BV Spaces. Let us first consider a function $f\in L_{loc}^1(\Omega)$, where $\Omega$ is an open subset of $\mathbb{R}^N$. One cannot,…
3x89g2
  • 7,542
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Proving the relationship $1 + r \leq \left(1 +\frac{r}{m}\right)^m$ for any $m \geq 1.$

I am currently trying to prove the following relationship $$1 + r \leq \left(1 +\frac{r}{m}\right)^m\quad \text{for any }m \geq 1.$$ Would you be so kind and provide some hints/solutions to the above?
Bober02
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Correct way of defining a mathematical object (linguistic)

I am writing my thesis and my advisor made a correction to the sentence below: Transitional Rule commonly denoted by $\phi$ is defined by the map $\Sigma^n \rightarrow \Sigma$. He has changed the sentence by changing the definite article the to…
Yousof
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What does rigoruous but non-technical mean?

Hi I find the above expression a bit confusing. I am considering buying a book and it says that it's a rigorous but non-technical introduction to optimal stochastic control. Could someone explain ? Is the book on Brownian Motion and stochastic…
user3503589
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What does "be the inclusion" mean?

Can anyone explain what the phrase means? To be specific, my notes has the phrase "let $f:A \rightarrow B $ be the inclusion". Does this mean the identity map?
jh4
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What does bimeasurable mean? Is an invertible transformation bimeasurable?

What exactly is the meaning of a bimeasurable transformation? I did not find a very clear answer to that. As far as I see it means that Borelsets are maped to Borelsets. So an invertible transformation is bimeasurable?
Salamo
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What is the coupling of two measures?

I know what means coupling for random variables, as explained here. But what is a coupling of measures?
user34632
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is there a discipline of mathematics that studies graphical versions of various operations?

What I am interested about is a discipline that deals with mathematical operations that can be done graphically, in this case meaning using some kind of "structures" that are manipulated to arrive at an answer. No number-symbols are used with these…
x457812
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