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Two questions:

(-1) Everyone I've spoke to says that you cannot have negative ATK, why? It's not in the rule book so it seems that if I could reduce the ATK of an opponent to become negative then in the event I attack them, my ATK would be applied then they would attack themselves (the value equal to the absolute value of their negative ATK value).

(∞) I've heard from a few sources that after the ATK points reach a certain value (over 9999 maybe? by any means possible) that the value becomes infinite, is this true? I realize there are some cards which are not legal for play which have infinite ATK values, but is there any rule that states a sufficiently high finite ATK "becomes" infinite.

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1) No, negative numbers are not possible on monsters. It is true that this is not explicitly stated in any of the official rulebooks. However, it is most common that such values in games refer to non-negative integers, and therefore it can be assumed that it is the case unless otherwise stated. It is the responsibility of the rulebook to explicitly state if negatives were allowed, not the other way around.

2) No. There is noting even remotely true about the statement, to the point of which the very concept seems rather random. It's possible that such a glitch might exist in one of the video games, and that your friend might have been referring to that. Even so, that is an unintentional (and theoretical) computer glitch, and does not reflect on the real game, which is not limited by such issues.

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Several games do allow attack values to be negative for purposes of calculating 'boosts' needed to get those values back to positive territory, but then just clamp them to zero for effect purposes. This is how Magic handles negative power on a creature, for instance: a creature that is, say, a -2/2 will deal zero damage (not '-2 damage') to an opponent or to other creatures , but a Giant Growth (+3/+3) will only make it a 1/5. – Steven Stadnicki Jul 21 '13 at 16:12
@StevenStadnicki This can be seen more as recalculating the total from scratch whenever it changes as opposed to going into negatives. – Southpaw Hare Jul 21 '13 at 19:59
I'm a mathematician so I know what natural numbers are... but there is no need to use equivocal language when this should be readable to any Yu-gi-oh player. – Squirtle Jul 21 '13 at 21:06
@Squirtle I am not intending to speak in any way that is harsh or insulting, nor do I think it should be interpreted that way. – Southpaw Hare Jul 21 '13 at 21:09
@Squirtle Your change is fine, but I'm going to still keep the link to the Wikipedia page. "Non-negative Integers" is a bolded title on that page, meaning that it is an alternative name for the same article and still applies. And as for the confusion of the term, that is what the link is for. – Southpaw Hare Jul 21 '13 at 21:12

I don't speak from the rules, but here goes.

I agreed that there should NOT be negative numbers. If there were, the rules would state it, and effects that have you damage yourself in the process would most likely include something involving a negative number. That said, this is opinion, and the absense of proof is not proof in and of itself.

Furthermore, the logic that they have to exist because 300-500+1000=800 not 300-500+1000=1000 is simple math. This is commutative. You can change the order of the numbers however you want, but the outcome is the same. (1000+300)-500=800

As far as infinity is concerned... I think this is just a situation where the ATK of a card becomes irrelevant. I'm not gonna bother doing the math if you get a 10,000 ATK beatstick. I only have 8000 Life Points at best, and you probably aren't attacking something over 2,000.

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Well this is precisely the point... should the point system of yugioh have a noncommutative geometry? I guess like in mathematics, you can have which ever case you want so long as it's agreed upon with the audience at hand – Squirtle Mar 30 '14 at 2:19
@Squirtle: Note that while they don't put everything somewhere, Konami and the creators of Yu-Gi-Oh! certainly do have an idea of how their rules work. You can agree upon whatever you like, this still doesn't change the rules of the game. Even if all players decided Monsters should be played in the Field Spell Card Zone, this would still not be correct, even if it doesn't specifically say so in the rules. Of course, if you're playing with your friends, you can agree on whatever house rule you like. – scenia Apr 1 '14 at 7:32
up vote -4 down vote accepted

(1) Negative numbers are allowed, because lack of evidence to say that something isn't allowed is not evidence that negative numbers are lacking (in the game). The very fact that it was not mentioned in the rule books suggests that it is allowed. The most natural explanation is that such a monster would directly attack its owner's life points if it were to attack another monster and it would be destroyed as well. Further, we must allow negative numbers for the following reason:

Suppose for a moment that we do allow them; now suppose that I reduce your ATK points to below zero (by whatever means). Now, suppose on your next turn you summon a monster or use a spell, so that you add ATK points to every monster (or just one); would it be fair for you to add those points as if you were at zero to start with.... absolutely not! You should first add enough points to raise the monster to zero ATK then apply the rest. As an example, suppose I lower your 300 ATK monster by -500, then on your turn you add +1,000 ATK to that monster, you are now at 800 ATK and not 1000 ATK.

As a corollary, monsters with 0 ATK can successfully attack negative ATK monsters and not be destroyed.

(2) As far as infinite numbers, I completely agree that no finite number "becomes" infinite at any point; I was merely told that it was a rule; it clearly is not.

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-1: The fact that something isn't mentioned in the rules for a game should not be construed as suggesting it's the intended outcome. Your argument that negative numbers must be allowed also doesn't hold water; see Steven's explanation of how it's handled in Magic (a comment on Southpaw's answer) for another much more sane possibility than inventing the rule that monsters attack their owners. (It's far more believable that the rules neglected to discuss negative numbers than that they omitted the rule that monsters can attack their owners in that way!) – Jefromi Jul 21 '13 at 21:57
Much more sane.... lol. – Squirtle Jul 21 '13 at 22:00
If two monsters with 0 ATK fight each other in attack mode, they are NOT destroyed. This is a special exception, and it IS in the official rules. – Southpaw Hare Jul 22 '13 at 2:36
Yeah corrected.... regardless, until I can hear a rule stating otherwise I will assume my answer suffices. – Squirtle Jul 22 '13 at 17:06
@Squirtle Your answer has no more backing it than Southpaw Hare's does, but there are a ton of comments easily discoverable on the internet agreeing with him. None of them link to official rules, but still, your answer is just your personal opinion about what the rules should be; assume what you like, but don't expect it to convince someone you're playing against. – Jefromi Jul 23 '13 at 1:11

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