N Noxide Sep 2009 158 3 May 13, 2010 #1 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?

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 Nov 2009 468 14 May 13, 2010 #2 Noxide said: 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? Click to expand... 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 Reactions: Noxide

Noxide said: 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? Click to expand... 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

N Noxide Sep 2009 158 3 May 13, 2010 #3 Can you give me an example of "how they relate in graphs with coordinates" I'm not sure what you mean by this.

Can you give me an example of "how they relate in graphs with coordinates" I'm not sure what you mean by this.

W Wilmer Dec 2007 3,184 558 Ottawa, Canada May 13, 2010 #4 Noxide said: Say we solve x^2 - 1 = 0 we get x = 1, -1 Click to expand... 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.... Reactions: Noxide

Noxide said: Say we solve x^2 - 1 = 0 we get x = 1, -1 Click to expand... 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....

undefined MHF Hall of Honor Mar 2010 2,340 821 Chicago May 13, 2010 #5 Noxide said: 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? Click to expand... Like the other have said, it means or. If it meant and, this would imply that -1 = 1. Reactions: Noxide

Noxide said: 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? Click to expand... Like the other have said, it means or. If it meant and, this would imply that -1 = 1.

N Noxide Sep 2009 158 3 May 13, 2010 #6 So it's the exclusive or then? i.e. one or the other but not both?

undefined MHF Hall of Honor Mar 2010 2,340 821 Chicago May 13, 2010 #7 Noxide said: So it's the exclusive or then? i.e. one or the other but not both? Click to expand... 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. Reactions: Noxide

Noxide said: So it's the exclusive or then? i.e. one or the other but not both? Click to expand... 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.

undefined MHF Hall of Honor Mar 2010 2,340 821 Chicago May 13, 2010 #8 Here is some formal notation for you. \(\displaystyle \begin{aligned}\text{D}\text{efine } f: \ &\mathbb{R} \rightarrow \mathbb{R} \\ &x \mapsto x^2-1 \end{aligned}\) \(\displaystyle \text{Then }f(x)=0 \iff x \in \{-1,1\}.\) Reactions: Noxide

Here is some formal notation for you. \(\displaystyle \begin{aligned}\text{D}\text{efine } f: \ &\mathbb{R} \rightarrow \mathbb{R} \\ &x \mapsto x^2-1 \end{aligned}\) \(\displaystyle \text{Then }f(x)=0 \iff x \in \{-1,1\}.\)

C CaptainBlack MHF Hall of Fame Nov 2005 14,972 5,271 someplace May 13, 2010 #9 Noxide said: 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? Click to expand... It is an informal notation indicating these are elements of a list (of solutions) CB Reactions: Noxide

Noxide said: 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? Click to expand... It is an informal notation indicating these are elements of a list (of solutions) CB

N Noxide Sep 2009 158 3 May 13, 2010 #10 undefined said: Here is some formal notation for you. \(\displaystyle \begin{aligned}\text{D}\text{efine } f: \ &\mathbb{R} \rightarrow \mathbb{R} \\ &x \mapsto x^2-1 \end{aligned}\) \(\displaystyle \text{Then }f(x)=0 \iff x \in \{-1,1\}.\) Click to expand... THANK YOU! This makes it a lot more clear!

undefined said: Here is some formal notation for you. \(\displaystyle \begin{aligned}\text{D}\text{efine } f: \ &\mathbb{R} \rightarrow \mathbb{R} \\ &x \mapsto x^2-1 \end{aligned}\) \(\displaystyle \text{Then }f(x)=0 \iff x \in \{-1,1\}.\) Click to expand... THANK YOU! This makes it a lot more clear!