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

• Jun 2nd 2012, 04:05 PM
Insect
[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?
• Jun 2nd 2012, 04:27 PM
Wilmer
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.
• Jun 2nd 2012, 04:30 PM
Insect
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.
• Jun 2nd 2012, 04:31 PM
Reckoner
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?
• Jun 2nd 2012, 04:38 PM
Insect
Re: Does this make sense? If x is greater than y...
^ Not at all. Guess I've got some reading to do!
• Jun 2nd 2012, 04:38 PM
emakarov
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.
• Jun 2nd 2012, 04:41 PM
Insect
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?
• Jun 2nd 2012, 05:14 PM
emakarov
Re: Does this make sense? If x is greater than y...
Yes, if x ≥ y and y ≥ x, then x = y.
• Jun 2nd 2012, 05:31 PM
Insect
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?