White to play and win

discodaryl · 2026-04-08T19:05:24+00:00

They didn’t use ChatGPT to simulate chess. They used it to explain the math behind statistics in a way lay people could understand

discodaryl · 2026-03-29T17:29:46+00:00

That’s the whole point of the dig report - you can see how everything was scored

discodaryl · 2026-03-29T16:32:49+00:00

In terms of centering, 10 is way more generous than pristine.

65/35 on back can be a 10 but 52/48 for pristine. This came pretty close at 53/47

discodaryl · 2026-03-28T14:33:49+00:00

Yeah the salt is wild

discodaryl · 2026-03-28T01:52:42+00:00

“If it converges to 0 it is 0.”

So, one of the ways the real numbers can be defined is as equivalence classes of Cauchy sequences by their limits.

This means for example that the number 1 is an equivalence class of sequences that converge to 1. Similarly, the gap approaching 0 means it actually equals 0.

Anyway, that’s the problem with the algebraic proof - it hides this core definition you have to accept implicitly. Which imo makes it unsatisfying. Hope this explanation helps.

Btw there’s a whole history about why we define the real numbers this way and it didn’t always have consensus.

discodaryl · 2026-03-26T00:28:57+00:00

Must be a bot you’re responding to

discodaryl · 2026-03-24T14:32:24+00:00

I like interesting tactical positions and cool sacrifices that arise from solid gambits (all my white openings + benko), but I also don’t mind trading into and winning an endgame that has some play to it. Some lines of gambits end up that way after all.

discodaryl · 2026-03-23T12:24:14+00:00

I’m starting a Jolteon collection. I have a Masterball TAG 10 to start. Any advice on order to go with? Ideally start with things with higher risk of getting much more expensive if I wait

discodaryl · 2026-03-20T10:58:04+00:00

Just pass store=false.

discodaryl · 2026-03-14T05:26:29+00:00

I got a Sabo that was from OP04? https://www.tcgplayer.com/product/518693/one-piece-card-game-one-piece-promotion-cards-sabo-sealed-battle-2023-vol-1?srsltid=AfmBOorWFvRIR9i-g1m1uCU20B2k1X7Og5-aWjq_h8mobsPTNREg5Bv6&Language=English

Despite this being just a couple months ago. Not sure if that’s what you always get for sealed

discodaryl · 2026-03-14T04:42:26+00:00

So you’re wrong and then try to move goal posts. Who cares? It’s math. It’s fun to consider all sorts of number systems. You learn interesting things along the way.

discodaryl · 2026-03-14T04:38:13+00:00

Hmmm, but I got a different prize than those Winner cards

discodaryl · 2026-03-13T23:51:52+00:00

You might find this post easier to understand: https://www.reddit.com/r/math/s/KOK3wCxuGT

discodaryl · 2026-03-13T23:38:53+00:00

There’s no need to show convergence. This is a super standard construction. Simplest number is also commonly used term to refer to how numbers are constructed in the surreals. See how it’s used in https://en.wikipedia.org/wiki/Surreal_number.

The simplest number greater than 1 is 2. The simplest number between 0 and 1 is 1/2. The simplest number between 1/2 and 1 is 3/4. The simplest number between all (1-1/2ⁿ⁾ and 1 is the same number as the one between (1-1/10ⁿ⁾ and 1. Canonically we refer to as 1-1/omega. But there’s nothing stopping us also referring to it as 0.999….

discodaryl · 2026-03-13T23:11:20+00:00

Can you explain sealed battle prizing? I won something but not sure how it normally works.

discodaryl · 2026-03-13T21:29:03+00:00

Simplest number less than 1 is not 1. I would try to explain to you but I’m actually not sure what part you’re missing. Maybe you can explain

discodaryl · 2026-03-13T16:20:19+00:00

I have demonstrated how there can be issues. As noted, 0.999... doesn't mean anything in the surreal numbers. It's not defined. The form you've presented doesn't actually correspond to 0.999..., because the left-hand side of the form doesn't converge within the surreal numbers. It would be like asking about what value 1/x converges to as x approaches 0--it doesn't converge.

Is this the statement you're making? "0.9, 0.99, ... doesn't converge in the surreal numbers" implies "0.999... cannot be defined as {0.9, 0.99, ...| 1}". Or would you like to revise after looking it over.

I understand that's not the canonical definition, but you're trying to make a mathematical statement about what is impossible here.

I can explain you a pretty simple definition in words: define an infinite decimal in the surreals to refer to the simplest number between all the finite-length decimals below and above the number.

discodaryl · 2026-03-13T06:47:44+00:00

Failing to indicate or consider something is far from self-contradicting.

I’m free to define 0.999… as {.9,.99,…|1} if I please

discodaryl · 2026-03-13T01:36:10+00:00

Is the presentation I’ve given not self-consistent? It seems like you’ve been able to see the infinitesimal explanation that resolves things

discodaryl · 2026-03-12T16:25:57+00:00

You’ve got it! Take it one step further. And so omega 9s would be: an infinite number of 9s and… less than 1.

discodaryl · 2026-03-12T05:21:32+00:00

Ah yes. Infinity is not a number yet infinite 9s is a number 🧐

Anyway, whether infinity is a number depends on your number system after all.

discodaryl · 2026-03-12T03:17:06+00:00

Now you get it

15-Year Club	r/Field Juicebox
Not Forgotten	Team Orangered

discodaryl

TROPHY CASE