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

  1. Jun 2, 2012 #1
    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. jcsd
  3. Jun 2, 2012 #2
    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 '[itex]\leq[/itex]' which means "less than or equal to." In that case x [itex]\leq[/itex] y and y [itex]\leq[/itex] 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
  4. Jun 2, 2012 #3
    ^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.
     
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