Theorem: The negative of every irrational number is irrational.
Proof:
1. Suppose there is some irrational number p such that -p is rational.
2. -p = m/n, where m and n are both integers and n ? 0
3. p = -m/n, where -m and n are both integers and n ? 0
4. p is rational, which is contradiction
Which of the following in the proper justification for line 2 in the above proof by
contradiction??
Contradictory supposition
Algebra
Definition of rational numbers
Closure of integers under negation