Smallest Rational Number Proof

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Can anybody help me out with solving this mathematical proof?

Prove the statement “There is no smallest rational number greater than 2” by contradiction.

Contradiction: There is a smallest rational number greater than 2.

I know the above is false because the smallest rational number greater than 2 is a fraction of a decimal 2.00…01 as it gets closer and closer to 2 (by adding more decimal places). Since you can get infinitely closer and closer to 2 there is no exact “smallest rational number”.

However, I'm not sure how to officially prove it.

Thanks in advance!