- #1
Mr Davis 97
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Homework Statement
If ##\forall \epsilon > 0 ## it follows that ##|a-b| < \epsilon##, then ##a=b##.
Homework Equations
The Attempt at a Solution
Proof by contraposition. Suppose that ##a \neq b##. We need to show that ##\exists \epsilon > 0## such that ##|a-b| \ge \epsilon##. Well, let ##\epsilon_0 = |a-b| > 0##. Since ##|a-b| \ge \epsilon_0##, we are done.
Is this proof okay? It doesn't seem very enlightening as to why the theorem is true...