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Math Help - Does this make sense? If x is greater than y...

  1. #1
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    [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?
    Last edited by Insect; June 2nd 2012 at 05:32 PM. Reason: Solved Problem.
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  2. #2
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    Re: Does this make sense? If x is greater than y...

    Quote Originally Posted by Insect View Post
    x > y
    y > x
    Impossible!

    Check your post and be CLEAR.
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    Re: Does this make sense? If x is greater than y...

    Quote Originally Posted by Wilmer View Post
    Impossible!

    Check your post and be CLEAR.
    I am assuming it is so.
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    Re: Does this make sense? If x is greater than y...

    Quote Originally Posted by Insect View Post
    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?
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    Re: Does this make sense? If x is greater than y...

    ^ Not at all. Guess I've got some reading to do!
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    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.
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    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?
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  8. #8
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    Re: Does this make sense? If x is greater than y...

    Yes, if x ≥ y and y ≥ x, then x = y.
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    Re: Does this make sense? If x is greater than y...

    Quote Originally Posted by emakarov View Post
    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?
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