Solution Found!
True or false: If a is irrational, then a -I is irrational
Chapter 31, Problem 31.23(choose chapter or problem)
QUESTION:
True or false: If a is irrational, then a -I is irrational.
Questions & Answers
QUESTION:
True or false: If a is irrational, then a -I is irrational.
ANSWER:Step 1 of 2
Proof: We use proof of contradiction, let there exists irrational number a, who's reciprocal is rational
Since 1/a is rational, then there exists integers p and q for which 1/a=p/q.
Since a is finite, we know that 1/a is not equal to zero, so p is not equal to zero. So 1/(1/a) exists.