## Give a mathematical proof by contradiction

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
jameshl2008
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### Give a mathematical proof by contradiction

For any real numbers a1, a2, a3, we must have that one of the numbers is less than or equal to the average (a1+a2+a3)/3.

Should I start by assuming the contra positive? Very confused.

stapel_eliz
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For any real numbers a1, a2, a3, we must have that one of the numbers is less than or equal to the average (a1+a2+a3)/3.

Should I start by assuming the contra positive? Very confused.
If your subject line ("Give a mathematical proof by contradiction") contains the instructions then, no, you should start by assuming the opposite of what is desired (and find an error in the results).

The contrapositive is a true statement "If not-B, then not-A" resulting from "reversing" the true statement "If A, then B". A contradiction proof tends to start along the lines of "A and not-B" and following the logic until a contradiction pops out.