Just a silly philosophical riddle/paradox, but people seem to like to discuss these sometimes.

Suppose there were a kind of ticket which could be redeemed once for any amount the owner likes up to, *but not including*, $100. (So it could be redeemed for $40, or for $99, or for $99.50, or even for $99.999993, but not $100). This is a philosophy question, not a real-world question, so let’s go ahead and assume money is infinitely divisible (yes, in the real world, people round at some point, and don’t worry too much about arbitrage exploiting the rounding).

How much is this ticket worth?

On the one hand, it’s clearly worth at least $40, and at least $99, and at least $99.50, and at least $99.999993, and so on. So it’s worth at least as much as every value less than $100.

On the other hand, it oughtn’t be worth as much as $100. Because no matter what, it will eventually be redeemed for less. So it’s worth less than $100.

But where does that leave its value?

[Note: I chose this phrasing in terms of money just because it was convenient. But it can be phrased in other terms just as easily; all that’s needed are a number of options with no best option]