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Homework Statement
Prove the following:
If x=y and y=z then x=z.
Now, this seems very obvious, and it is without a doubt correct. However, I am curious as to if the following proof is correct.
Homework Equations
The Attempt at a Solution
Assume x does not equal to z, so that means two cases:
Case 1) x>z, so z-x<0 and since x=y, z-y<0 which is a contradiction.
Case 2) z>x, so x-z<0 and since y=z or x=y ( I can use either), that means x-y<0 which is a contradiction. Therefore it has to be that if x=y and y=z then x=z.
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