Thread: Numbers in a big bag

If I put all the numbers between 0 and 1 into a big bag (Yes, a very big bag)

And that I ask you to pick one,

what would be the probability for you to pick a transcendental number over an algebraic number?

(As you know, there is in the bag an infinite number of algebraic numbers and an infinite number of transcendental numbers )

Originally Posted by LChenier

If I put all the numbers between 0 and 1 into a big bag.
And that I ask you to pick one, what would be the probability for you to pick a transcendental number over an algebraic number?

The set of algebraic numbers is countable. Therefore the set of transcendental numbers must be uncountable.