# Can someone tell me if this makes sense? (Equalities question)

1. Jun 2, 2012

### AnInsect

x>or=y
y>or=x
x=y+z
y=x+z

y=y+z+z
0=2z
0=z

x=y+z
x=y+0
x=y

I think what I just said is that if x is greater than y and y is greater than x, they must be greater than eachother by zero, thus proving they are equal. It also works if x is greater than y by z and y is greater than x by say q (though in the end both q and z are zero).

Does this make any sense?

Last edited: Jun 2, 2012
2. Jun 2, 2012

### SteveL27

x > y precludes x = y by convention. So x > y and y > x is a logical contradiction, if by '<' you intend the usual meaning.

Your conclusion is valid if you use the symbol '$\leq$' which means "less than or equal to." In that case x $\leq$ y and y $\leq$ x do indeed imply that x = y. However I'm a little confused by your proof. What is z, is it supposed to be a constant? You essentially have the right idea but you need to make it a little more clear.

Last edited: Jun 2, 2012
3. Jun 2, 2012

### AnInsect

^Thank you for the clarification! I noticed that too, but then it sort of makes the entire thing redundant doesn't it? Ah well, journey's better than the destination I guess.

^z is any real number. You know, just a variable representing the difference between x and y.