I love "destroy target player", but it feels tacked on on a card that doesn't destroy anything else. I'm not sure if there was a way of doing that better.

I notice, the cards overall seem a bit less out there than previous un sets. They're still un-rules-y, but there's less art exploding all over the text box, and less disregard for normal templating (like the augment creature which can augment at instant speed, they spell it out in rules text, not just change the reminder text). Even if the rules still need a similar amount of careful FAQ-ing :)

Ah! They introduced transcendental numbers (pi damage, although you can round to 2 s.f. if it's easier to count).

And Rosewater makes a ruling about infinity life -- it doesn't work like an ordinal, or a cardinal, which I think would be more interesting, it's just infinity life minus infinity damage is still infinity, infinity plus infinity is still infinity

Did he make a ruling about what happens if you have minus infinity life and then gain infinity life?

Not specifically, but I can't imagine minus infinity gaining infinity is different to infinity losing infinity, i.e. both stay the same.

The choice is nothing but arbitrary, it seems to me.

You mean, to use that version of arithmetic, or what the particular results are?

It seems to follow "when you gain infinity life, lose infinity life, do anything else infinite, the result is the same as doing it for 1, but repeated an infinite number of times" rules, which is (I think?) unambiguous, but sometimes unsatisfying.

If you have negative infinity life and get dealt positive infinity damage, the answer is you end up with zero life. Infinity plus its negative is zero. I don't think Magic would ignore such a fundamental rule in mathematics.

I'm not entirely convinced.

Rosewater says, if you have infinity life and take infinity damage, you're still on infinity. Is negative infinity different? I don't know if the way Rosewater chose right, but that's what he says in the FAQ.

There's not a single way of dealing with infinity which is appropriate in all circumstances. If you treat infinity as a number, and say "inf - inf = 0" then you break equations like "x + 1 - x = 1" when x is infinity. If you say "inf - inf = inf" then you break "x - x = 0". Other compromises break other assumptions.

If you allow infinity at all, you get some weirdness. E.g. floating point arithmetic on computers, you get NaN ("Not a number") when you try to calculate INF - INF, -INF + INF, INF/INF or 0/0. The reason being, those are operations you might sometimes expect to be reversible, and sometimes not.

That doesn't work in magic, because your life might be INF but can't really be NaN. So they picked one. I'd prefer an implementation that allowed you do take infinite life to zero SOMEHOW (I have some in mind but haven't played them) but I understand that wouldn't be a good choice for most players who aren't mathematicians.

So they had to pick some interpretation. I think allowing inf - inf to be 0 might be a more fun choice for playing magic. But I don't think it's more mathematically correct (you can justify inf - inf being any other finite number or inf, equally well).

If you assume cardinality applies, you can make infinite tokens somehow, devour them with Thromok, and deal infinity² damage. That is undeniably larger than infinity

Hah! Right, Thromok is very useful for this, I hadn't realised that.

But I'm not sure that works for dealing damage to someone with infinite life. If you define a notion of subtraction like "subtract 1, that many times", then subtracting 1 from ω leaves ω, so however many infinite times you do that, ω, ω+1, ω², all the way up until 2^ω, it still leaves ω.

Whereas if you define subtraction to consider both ordinals at once, then ω - ω (or ω - ω+1) would get to zero anyway.

Is there a case where ω² works better?

I've looked for magic rules which would naturally generate an uncountable infinity, but I don't think I found any.

­Mary O'Kill's switch and combined creatures are two things I'm going to be exploring in the future. Its something many people dabbled into (the latter more than the former) and it's often been more of a matter of choosing one option over the other and with a semi-canon reference mechanic a lot of this is just easier to handwave.

I'm quite happy about where Very Cryptic Command is going. And alternate illustrations are neat, too.