What is the probability that a random number is irrational/transcendental? Are there infinitely more transcendental numbers than irrational numbers?

Howard Nelson

Howard Nelson

Answered question

2022-11-06

What is the probability that a random number is irrational/transcendental? Are there infinitely more transcendental numbers than irrational numbers?

Answer & Explanation

levraijournalk1o

levraijournalk1o

Beginner2022-11-07Added 10 answers

The rational numbers are merely countably infinite, while the real numbers are uncountably infinite, so the probability of a number in the interval [ 0 , 1 ] being irrational is "certainty".
The algebraic numbers are also countably infinite, so the probability of a number in that interval being transcendental is also "certainty".

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?