[gentaro]

>> The idea is that by picking a random real number C, there is a chance it will fall between A and B over time, no matter how the other person picks their numbers A and B.

But for any two finite numbers, A and B, the chance that C will fall between them if selected from an infinite range is 1/infinity (or 0).

[greenbay20]

>> But for any two finite numbers, A and B, the chance that C will fall between them if selected from an infinite range is 1/infinity (or 0).

I think you're assuming we pick C uniformly at random from an infinite range, but this is not possible. In general, the claim is not true: consider picking C from a sample of a standard normal, if A = -B = 2 then with >95% C will lie between A and B.

[lonelappde]

It's not 0, it's "an unknown positive number" drawn arbitrarily from a set whose lower bound is 0. It's practically 0, but it's some fixed positive number for every instance of the game.

It's equivalent to this much simpler game: "I am going to give you a positive real-number amount of dollars." No matter what I do, you will win money playing this game, guaranteed! Now, how much would you pay to play this game? $0, because for any amount you'd pay to play, I could arbitrarily choose to give you less in winnings.

Like most problems involving infinity, it's unintuitive/paradoxical because it pretends to model a physically plausible scenario but actually doesn't.

[kgwgk]

Would you say that the value of the infinite sum 1/2 + 1/4 + 1/8 + ... is 1 or that it is an unknown number?

The probability that a random number uniformly drawn from the real line is between 42 and 43 is zero in the same way that “the probability that a random real number selected uniformly from the interval [0 1] is pi/4” is zero.

[speedplane]

> Would you say that the value of the infinite sum 1/2 + 1/4 + 1/8 + ... is 1 or that it is an unknown number?

Integral of 1/2^n ... got that no problem.

I took AB Calculus in high school, three semesters of calculus in college, and a bunch of calculus heavy linear algebra. I’m certain that I knew how to integrate that thing at some point... it’s pretty sad that now I can only stare at it blankly and at best lean heavily on Wikipedia to find an answer.

[kgwgk]

What I wrote is an infinite series and it’s much simpler to solve than the integral:

https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%...

[speedplane]

Ha, yup, citing a Wikipedia article too. At least I’m not alone.