Question

Prove that if x is irrational then 1/x is irrational

Answer 1

i suppose first step is to assume x is rational and try to prove by contradiction...

Answer 2

so

x = a/b where a/b is in simplest terms

Answer 3

nevermind....this is wrong....

Answer 4

i would go by contadiction,
let us assume x is irrational, then 1/x is rational.(we'll prove this incorrect)
if 1/x is rational, what it can be written as?

Answer 5

i assume b/a where b/a is in simplest form

Answer 6

same thing in different words, 1/x = b/a where a,b are integers
then what is x from here?

Answer 7

a/b

Answer 8

oh...

Answer 9

i see

Answer 10

since, a and b are integers, a/b = x is rational

Answer 11

is it possible to do contradiction using x = a/b?

Answer 12

then u will prove that if x is rational, 1/x is also rational

Answer 13

shouldn't it be 1/x is irrational?

Answer 14

oh...i see

Answer 15

if x is rational, 1/x is also rational