Proves by Contradiction

Question 1

General steps for proves by contradiction? 5•

Answer 1

•Make the statement precise (e.g., a number is irrational if it is not rational)
•Make a mathematical definition of the opposing statement (e.g., x = y for the false assumption, assuming that the false assumption is correct)
•Create a mathematical statement in which we have to reject the opposing statement, false assumption ( x =! y)

If you have to prove a negation, then you prove by contradiction

•Assume the opposite (assume that x = y)
•Derive the proof so that at the end, there is a dead end that implies that the assumption cannot be held true.