Mathematical Meaning of commas

Sep 2009
158
3
I know commas are used to separate 2 or more elements in a list but what is their mathematical meaning?

Say we solve x^2 - 1 = 0
we get x = 1, -1

Does that mean x is 1 and -1?

Does that mean x is either -1 or 1 or both?
 
Nov 2009
468
14
I know commas are used to separate 2 or more elements in a list but what is their mathematical meaning?

Say we solve x^2 - 1 = 0
we get x = 1, -1

Does that mean x is 1 and -1?

Does that mean x is either -1 or 1 or both?

It's used as or, however it may differ from scenario to scenario, for example I am unsure of how they relate in graphs with coordinates
 
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Sep 2009
158
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Can you give me an example of "how they relate in graphs with coordinates"

I'm not sure what you mean by this.
 
Dec 2007
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Say we solve x^2 - 1 = 0
we get x = 1, -1
No, we get (x+1)(x-1) = 0 ; so x+1 = 0 OR x-1 = 0 ; x = -1 OR x = 1

x cannot equal 2 different values all at once....
 
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undefined

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I know commas are used to separate 2 or more elements in a list but what is their mathematical meaning?

Say we solve x^2 - 1 = 0
we get x = 1, -1

Does that mean x is 1 and -1?

Does that mean x is either -1 or 1 or both?
Like the other have said, it means or.

If it meant and, this would imply that -1 = 1.
 
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Sep 2009
158
3
So it's the exclusive or then?
i.e. one or the other but not both?
 

undefined

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So it's the exclusive or then?
i.e. one or the other but not both?
I was thinking of specifying that but thought it was clear from context.

Yes, exclusive or. Because if we allow for possibility of and, then we get -1 = 1.
 
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undefined

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Here is some formal notation for you.

\(\displaystyle \begin{aligned}\text{D}\text{efine } f: \ &\mathbb{R} \rightarrow \mathbb{R} \\ &x \mapsto x^2-1 \end{aligned}\)

\(\displaystyle \text{Then }f(x)=0 \iff x \in \{-1,1\}.\)
 
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CaptainBlack

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I know commas are used to separate 2 or more elements in a list but what is their mathematical meaning?

Say we solve x^2 - 1 = 0
we get x = 1, -1

Does that mean x is 1 and -1?

Does that mean x is either -1 or 1 or both?
It is an informal notation indicating these are elements of a list (of solutions)

CB
 
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Sep 2009
158
3
Here is some formal notation for you.

\(\displaystyle \begin{aligned}\text{D}\text{efine } f: \ &\mathbb{R} \rightarrow \mathbb{R} \\ &x \mapsto x^2-1 \end{aligned}\)

\(\displaystyle \text{Then }f(x)=0 \iff x \in \{-1,1\}.\)

THANK YOU!

This makes it a lot more clear!