1. difference (set)

Why the equation in the picture is true?
http://mathhelpforum.com/attachments...difference.png

2. Re: difference (set)

$$\mathbb{N}_{\text{odd}} - \mathbb{N}_{\text{even}} = \mathbb{N}_{\text{odd}} \cap \left(\mathbb{N}_{\text{even}}\right)^c = \mathbb{N}_{\text{odd}} \cap \mathbb{N}_{\text{odd}} = \mathbb{N}_{\text{odd}} = \left\{ n \in \mathbb{N}_{\text{odd}}: n \text{ is not even} \right\}$$

3. Re: difference (set)

Another way of looking at it- the set of even numbers does not contain any odd numbers so removing all the even numbers from the set of all odd numbers does not remove any numbers at all.

4. Re: difference (set)

Originally Posted by HallsofIvy
Another way of looking at it- the set of even numbers does not contain any odd numbers so removing all the even numbers from the set of all odd numbers does not remove any numbers at all.
The reason I prefer the above is that unless we know that $\mathscr{U}=\mathbb{N}$ (i.e. the universe) it does no follow that $\mathbb{N}_{\text{even}}^c=\mathbb{N}_{\text{odd} }$