Question

I was asked to find the domain of a function. My answer was x<0 x>0. According to my teacher the answer is correct but I am missing the "or" symbol between the inequalities. Her exact words were "place the "or" symbol between the algebraic inequalities".
Can someone please tell me what she is talking about? Thanks!

Answer 1

Well if x is less than zero it can't also be greater than zero. That's just nonsense, unless you mean it's either one.

Answer 2

I'm taller than my little brother. My little brother is taller than me.

I am taller than my little brother or my little brother is taller than me.

Which sentence makes sense to you?

Answer 3

The second one makes more sense. But she said my answer was right....except for the "or" symbol.

Answer 4

The second one doesn't make more sense, it's the only one that makes sense. The first sentence is nonsense. Think about why this is. The difference between the two sentences is simply an "or".

Answer 5

Oh! I understand it better now. So, it's x can EITHER be greater than OR less than 0. So which symbol do I use?

Answer 6

Ahh, so if she wants you to use a symbol, that would be this one:

V

it looks like a capital vee.

so something like this will do:

x<0 V x>0

Answer 7

Is it something like that U looking thing, like this (-, 0)U(0, )?

Answer 8

Yeah, actually they're very similar! The V is a logical "or" and is used to define the set theory "union". So depending on if you're considering the answer in terms of sets or logical connectives, you can actually end up using either. For instance, to say the same thing in set theory,

\[x \in (-\infty,0)\cup(0,\infty)\]

Answer 9

Got it!! Thanks so much!!

Answer 10

Cool. =)