Purchase Solution

# Real Analysis of Irrational Numbers

Not what you're looking for?

Proof:
Given any two real numbers a<b ,there exists an irrational number t satisfying a<t<b

##### Solution Summary

The expert provides a proof for given any two real numbers a<b ,there exists an irrational number t satisfying a<t<b

##### Solution Preview

Let decimal expansions of two real numbers a and b (a<b) first differ in the nth digit.
First, if the nth digit is not the last digit of b, consider the number bn obtained from b by cutting all the digits of b after the nth, then: a<bn<b.
there is two cases here:
(1)b has non zero digits after the nth, Append to bn one zero digit, give the result number to t;
(2)b has zero digits right after the nth. Let bm be ...

##### Free BrainMass Quizzes

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Probability Quiz

Some questions on probability