[SOLVED] Does this make sense? If x is greater than or equal to y...

Assume x is greater than y by z and y is greater than x by z (seems impossible, and it might very well be, but read on)

x> or equal to y

y> or equal to 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?

Re: Does this make sense? If x is greater than y...

Quote:

Originally Posted by

**Insect** x > y

y > x

Impossible!

Check your post and be CLEAR.

Re: Does this make sense? If x is greater than y...

Quote:

Originally Posted by

**Wilmer** Impossible!

Check your post and be CLEAR.

I am assuming it is so.

Re: Does this make sense? If x is greater than y...

Quote:

Originally Posted by

**Insect** x>y

y>x

...

Does this make any sense?

Not unless you're using a strange definition of "greater than" (or you used the wrong symbol). Are you familiar with the Law of Trichotomy?

Re: Does this make sense? If x is greater than y...

^ Not at all. Guess I've got some reading to do!

Re: Does this make sense? If x is greater than y...

The fact that x = y + z for z ≥ 0 is equivalent to x ≥ y, not x > y. You proved correctly that if x ≥ y and y ≥ x, then x = y. This fact is expressed by saying that ≥ is *antisymmetric*. In contrast, x > y and y > x is impossible. This means that > is *asymmetric*.

Re: Does this make sense? If x is greater than y...

^ Ah I see.

So for x is greater than or equal to y, and y is greater than or equal to x, this would ring true?

Re: Does this make sense? If x is greater than y...

Yes, if x ≥ y and y ≥ x, then x = y.

Re: Does this make sense? If x is greater than y...

Quote:

Originally Posted by

**emakarov** Yes, if x ≥ y and y ≥ x, then x = y.

Well that's kind of redundant then.

But still, thank you for the help! I was just curious you know?