If you pick a number between 0 and 1 its going to either be a rational number, or is going to use a known irrational number (pi or sqrt(5)). In both cases it can be guessed in a finite number of guesses.
That's not true. The set of numbers between 0 and 1 is uncountable, which means that has a cardinality bigger than the natural numbers, ie: you can't build a bijection between [0, 1] and the natural numbers. Therefore, to fully specify any number in [0, 1] you'll need an infinite number of guesses.
There's an uncountable number of numbers between 0 and 1, but you, a human, can only pick from a countable subset of those.
But the number picker specified the number in their head to themselves before the game began.
Re:Twenty questions is a weird game
by thaumasiotes on Tuesday November 15, 2022 @06:39AM
(#33607960)
> If you choose a random number between 0 and 1 you'll need an infinite number of questions to guess the number.
How would you do that?
I don't think that's true. If you choose a random number between 0 and 1 you'll need an infinite number of questions to guess the number.