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is the symbol for Infinity, which has been used in a few exceptionally rare cases in the anime and manga as a monster's ATK or DEF value.

Strictly speaking, ∞ is not actually a number, but rather the concept of a value greater than any number. A monster with ∞ ATK cannot be destroyed by battle unless it battles another monster that also has ∞ ATK (and both are in Attack Position), in which case the two would destroy each other in a Double KO. If a monster with ∞ ATK attacked another Attack Position monster with non-infinite ATK, the controller of the latter would take an infinite amount of battle damage, instantly dropping their Life Points to 0.

Anime

  • One of the effects of "Template:Anime" is to increase its ATK to ∞ by Tributing 2 monsters. This was used a total of three times in the anime:
    • In episode 139, Yami Yugi used "Soul Taker" to Tribute Yami Marik's "Egyptian God Slime" for the effect of "Obelisk". By Battle City mechanics, "Slime" was able to count as two Tributes since it was a Fusion Monster made of two Fusion Materials. The ATK of "Obelisk" then became ∞, and Yami Yugi attempted to destroy Yami Marik's "Template:Anime" by battle to win the Duel. However, Yami Marik negated the attack with "Class System".
    • Twice in Yu-Gi-Oh! The Pyramid of Light, Yami Yugi Tributed "Template:Anime" and "The Winged Dragon of Ra" to make the ATK of "Obelisk" ∞. The first time, it was used to destroy Kaiba's "Template:Anime", inflicting an infinite amount of battle damage to Kaiba and causing him to lose the Duel. The second time, it was used to destroy Anubis's "Template:Anime" with the same result.
  • "Divine Serpent Geh" has an ATK of ∞. In episode 181, Dartz used this monster to destroy Yami Yugi's "Template:Anime", inflicting an infinite amount of battle damage to him and dropping his Life Points to 0.
  • In episode 182, Yami Yugi used the effects of "Template:Anime" and "Template:Anime" to form an infinite loop where the ATK of "Hermos" would be continuously multiplied. By anime mechanics, this caused the ATK of "Hermos" to become ∞. He then used the effect of "Legendary Knight Timaeus", absorbing "Critias" and "Hermos" to Summon "Template:Anime". Since "Knight of Destiny's" ATK is equal to the combined ATK of the absorbed monsters, its ATK became ∞ as well. It then destroyed Dartz's "Divine Serpent Geh" in battle.

Manga

  • In Yu-Gi-Oh! R - Duel Round 042, Template:Manga used the effect of "Obelisk the Tormentor" to increase its ATK to ∞. However, his opponent, Yako Tenma, controlled "Template:Manga", whose effect would make its own ATK and DEF equal to that of the strongest monster on the field + 1. This caused the ATK and DEF of "The Wicked Avatar" to become ∞ as well. True to actual mathematics, the two ATK values were treated as equal to each other (∞ + 1 = ∞ and is not greater than ∞), and the two monsters were later able to destroy each other in battle in a Double KO.

Trivia

  • There has not yet been an instance in the anime or manga where a player has achieved an infinite number of Life Points, although it would be theoretically possible by simply activating a card such as "Mystik Wok" on a monster with ∞ ATK or DEF.
  • No monster with ∞ ATK or DEF has ever been seen in Defense Position. Presumably, a Defense Position monster with ∞ DEF would be impossible to destroy by battle, as there would be no way for any monster to have an ATK higher than its DEF.
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