1.- Prove that the set of irrational numbers is uncountable by
using the Nested Intervals Property.
2.- Apply the definition of convergent sequence, Ratio Test or
Squeeze Theorem to prove that a given sequence converges.
3.- Use the Divergence Criterion for Sub-sequences to prove that
a given sequence does not converge.
Subject: Real Analysis
PROOFS:
1. State the prove The Density Theorem for Rational Numbers
2. Prove that irrational numbers are dense in the set of real numbers
3. Prove that rational numbers are countable
4. Prove that real numbers are uncountable
5. Prove that square root of 2 is irrational
1. Prove that the Cantor set contains no intervals.
2. Prove: If x is an element of the Cantor set, then there is a
sequence Xn of elements from the Cantor set converging
to x.
Prove that √3 is irrational using contradiction. You can use
problem 4 as a lemma for this.
Problem 4, for context is
Prove that if n2 is divisible by 3, then n is
divisible by 3.