Question: Proof that ?2 is irrational.
Answer: Assume that ?2 can be written as a/b where a and b are positive a and b ? 0
?2 = a/b
2 = a2/b2
2b2= a2
2b2 - a2 = 0
[(?2)b - a][(?2)b + a] = 0
(?2)b = a and -a
? reductio ad absurdum since:
(1) A number can't equal two different integers (2) A number can't be positive and negative (3) We know that ?2 is +ve and we assume that b is +ve and multiplying two positive numbers gives a positive result.
Just looking to learn and see where I'm being retarded. Thanks in advance
Answer: Assume that ?2 can be written as a/b where a and b are positive a and b ? 0
?2 = a/b
2 = a2/b2
2b2= a2
2b2 - a2 = 0
[(?2)b - a][(?2)b + a] = 0
(?2)b = a and -a
? reductio ad absurdum since:
(1) A number can't equal two different integers (2) A number can't be positive and negative (3) We know that ?2 is +ve and we assume that b is +ve and multiplying two positive numbers gives a positive result.
Just looking to learn and see where I'm being retarded. Thanks in advance
