Mampac
New member
- Joined
- Nov 20, 2019
- Messages
- 48
G'day,
In order to prove something, I need to show that if x2 − y2 = y2 − x2 and y2 − x2 = x2 − y2, then x = y. (proving a relation is antisymmetric)
I do realize this is VERY easy and evident, but i need to prove it algebraically. the thing is if i take a look at the first two statements, i get x2 = y2, which doesn't necessarily mean x = y, since if i take a square root it gives +-.
If i substitute right-hand side of second supposition for the right-hand side of the first one, i get x2 − y2 = x2 − y2 which will just cancel everything out and leave 0 = 0 which is true.
My question is: does this mean x = y? or what else I need to do?
In order to prove something, I need to show that if x2 − y2 = y2 − x2 and y2 − x2 = x2 − y2, then x = y. (proving a relation is antisymmetric)
I do realize this is VERY easy and evident, but i need to prove it algebraically. the thing is if i take a look at the first two statements, i get x2 = y2, which doesn't necessarily mean x = y, since if i take a square root it gives +-.
If i substitute right-hand side of second supposition for the right-hand side of the first one, i get x2 − y2 = x2 − y2 which will just cancel everything out and leave 0 = 0 which is true.
My question is: does this mean x = y? or what else I need to do?