Then you probably haven’t made a DoV due to that:

If a Pawn (other than the King) believes that they have achieved victory in the current Dynasty

(And arguably neither have I due to my doubts lol)

Hrm, alteratively we could go full philosophical and write an infinite amount of zeros in a conlang lol

Hmm, the S-Treasure is defined as any text string one of the Kings “hides” (in practice they discretely post it) in the listed locations that contains the string detailed in Unnamed Rule. So it defiantly can’t be an infinite string since it would be impossible to post it anywhere.

well it could be an infinite string but that just means nobody can post it in their blogpost, which is a requirement achieving victory, due to the character limit on Expression Engine.

[Cuddlebeam] So long as we believed it at the time we posted it. I still believe mine, it just seemed pragmatic to try it again with spacing in case a consensus emerged that spacing mattered.

[card] A rule that said “X is an infinite string. The King must post X to the blog.” would not make the definition of X invalid, it would just make it impossible to post it. And I think there’s plenty of precedent for people summarising lengthy or boring announcements of gamestate, so long as it’s completely unambiguous as to what they’re expressing.

“An infinitely long string of zeroes followed by…” is mathematically impossible, isn’t it?

Infinity has some eldritch mathematical bullshit to it but it’s not impossible for a string like that to exist.

Imagine we have some sort of Cartesian paper and we put at (0,0) the start of the string ” Super Treasure.”, and since that has 17 characters, lets say it extends all the way to (0,17)

That’s all nice and finite but then in the other direction, we start putting an infinite amount of zeros.

Of course, all the way in (0,-infinity) it could seem pretty hard to write the string of ” Super Treasure.”, but all the way back in (0,0) to (0,17) it’s perfectly fine. Infinity only needs to extend in one direction to be “infinite”, if we “anchor” it on one of the zeros it could seem hard to have the “Super Treasure.” at the end of the chain of it because that would mean we’d have some sort of “last zero” and that’s impossible. But we can work around it.

But yeah infinity is bullshit lol.

The “infinite zeros to the left” construction makes alphabetical sorting undefined: you need to look at the first letter to even begin deciding whether it comes before or after something else, and there is no first letter anymore with infinite left-zeros.

Not necessarily, there’s workarounds. We don’t need to know the first letter at all. We order periodic fractions just fine like 0.333… > 0.222… > 0.14444 etc, it would be the same for ordering expect we’re just writing them flipped around when it comes to the infinite sequence.

So

“...0000 Super Treasure.” would come before “...1111 Super Treasure.” and so on.

How do you know “...0000 Super Treasure.” comes before “...1111 Super Treasure” without defining a new way to alphabetically order that doesn’t need to look at the left side first?

We can order infinitely-long decimal representations because we eventually, in finite steps, come to a digit pair that differ, allowing them to be ordered. For 0.333… > 0.222… we only need to look at the first 3 and first 2 to know it’s the case. Note that it’s not the case using standard real numbers that 0.000…001 > 0.000…

If we have 0tomato and 1tomato, we know that 0tomato will come before 1tomato, yes? What about 00tomato and 11tomato? Well, 00tomato is still fist. And if we do it with three zeros and three ones? Still first. Four zeros and four ones? Still first. Any X integer of zeros and ones? Still first. At the limit to infinity (when adding the same to each and then comparing repeatedly forever), it would still be first.

Proof by induction doesn’t work in the limit to infinity. A counterexample would be that 1 is finite, and for any finite n, n+1 is finite, therefore in the limit to infinity, infinity is finite.

Well a simpler way to see it could be that 00000… followed by whatever will always come before a 11111…. followed by whatever.

(although that doesn’t really prove that “...0000 Super Treasure” and “...1111 Super Treasure” exist and are orderable themselves because I chose a different “anchor” lol)

This doesn’t quite make mathematic sense, since the greater than is using the alphabetical ordering and the strings are in there; however it demonstrates a way to compare possible default ordering values in step. Although this is the same anchor as Cuddlebeam’s example, you could change the dots to be on the other side as long as the repeated zeros or ones don’t change.

Another potential issue with infinite zeros to the left is that, using a period to represent the anchor point, can “...0000.supertreasure” still be beaten by “...0000.0supertreasure”?

So I’m absent 3 days following a long period of low activity, and come back to find multiple scam attempts (already resolved) and discussions on infinity? Rough :D. (but I was expecting this since Cuddlebeam’s proposal did look a lot like a pandora’s box of scams :D)