# Mathematical Meaning of commas

#### Noxide

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?

#### Mukilab

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

• Noxide

#### Noxide

Can you give me an example of "how they relate in graphs with coordinates"

I'm not sure what you mean by this.

#### Wilmer

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....

• Noxide

#### undefined

MHF Hall of Honor
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.

• Noxide

#### Noxide

So it's the exclusive or then?
i.e. one or the other but not both?

#### undefined

MHF Hall of Honor
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.

• Noxide

#### undefined

MHF Hall of Honor
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}

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

• Noxide

#### CaptainBlack

MHF Hall of Fame
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

• Noxide

#### Noxide

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!