- #1
cragar
- 2,552
- 3
Homework Statement
Given any 2 reals a<b there exists an irrational number t such that
a<t<b . It tells us to use a theorem that states there is a rational number between any 2 reals.
The Attempt at a Solution
so If we use this and pick reals of the form p=a-√2 and q=b-√2
so now we have a-√2<t<b-√2 , and t is a rational number. then we add √2
to everything so we get a<t+√2<b
so now t+√2 is irrational , so now we have an irrational between any 2 reals.