How to prove a number is irrational?
Understand the Problem
The question is asking for methods or techniques to prove that a particular number cannot be expressed as a fraction of two integers, meaning it is irrational. This involves understanding properties of numbers and potentially providing examples or logical reasoning.
Answer
Assume the number is rational and derive a contradiction.
To prove a number is irrational, assume it is rational and derive a contradiction.
Answer for screen readers
To prove a number is irrational, assume it is rational and derive a contradiction.
More Information
One famous example is the proof that √2 is irrational, which involves assuming √2 is rational, writing it as √2 = p/q, and showing that p and q must both be even, which contradicts the assumption that the fraction is in its simplest form.
Tips
A common mistake is not clearly showing how the contradiction arises. Make sure to detail the steps that lead to the contradiction.
Sources
- Proving Irrationality - number theory - math.stackexchange.com
- What is the process for proving that a number is irrational? - quora.com
- A proof that the square root of 2 is irrational - homeschoolmath.net
