Modify the proof of T 247 to show that there exists a positi

Modify the proof of T. 2.4.7 to show that there exists a positive real number y such that y^3 =2. (real analysis)

Solution

Given that y^3=2

y³=2

Taking the power of 1/3 on bothsides.

(y³)^1/3=2^1/3

y^3*1/3=2^1/3

y=2^1/3

2^1/3 is a positive number.

2^1/3 is a irrational number.

The numbers which are either rational or irrational are Real numbers.

Therefore, y is a positive real number.