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.
- One of the effects of "Obelisk the Tormentor" is to increase its ATK to ∞ by Tributing 2 monsters. This was shown on-screen 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 "The Winged Dragon of Ra" 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 "Slifer the Sky Dragon" and "The Winged Dragon of Ra" to make the ATK of "Obelisk" ∞. The first time, it was used to destroy Kaiba's "Blue-Eyes Ultimate Dragon", 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 "Theinen the Great Sphinx" with the same result.
- "Divine Serpent Geh" has an ATK of ∞. In episode 181, Dartz used this monster to destroy Yami Yugi's "Legendary Knight Timaeus", inflicting an infinite amount of battle damage to him and dropping his Life Points to 0. However, Yami Yugi activated "Relay Soul" to Special Summon "Dark Magician Girl" and be able to continue the Duel until she was destroyed.
- In episode 182, Yami Yugi used the effects of "Legendary Knight Critias" and "Legendary Knight Hermos" 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 "Timaeus the Knight of Destiny". Since "Knight of Destiny's" ATK is equal to the combined ATK of the absorbed monsters, its ATK became ∞ as well. It then battled Dartz's "Divine Serpent Geh", destroying both monsters in a Double KO. (The effect of "Knight of Destiny" then Special Summoned the 3 "Legendary Knights" back to the field.)
- At one point when the five pieces of "Exodia" were gathered, the complete "Exodia" was shown as a monster with an ATK of ∞, representing "Exodia's" automatic victory condition.
- In Yu-Gi-Oh! R - Duel Round 042, Dark Yugi used the effect of "Obelisk the Tormentor" to increase its ATK to ∞. However, his opponent, Yako Tenma, controlled "The Wicked Avatar", 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 math, the two ATK values were treated as equal to each other (∞ + 1 = ∞ and is not greater than ∞); shortly after, with the aid of "Divine Evolution", the two monsters were able to destroy each other in battle in a Double KO.
- No monster with ∞ ATK or DEF has ever been seen in Defense Position.
- 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.
- Technically speaking, Yami Yugi's maneuver with "Legendary Knight Hermos" would have yielded an ATK greater than ∞, if ∞ has its usual meaning of the smallest possible infinity. In math, it can be proven that adding or multiplying ∞ by any number (even multiplying ∞ by itself) yields a value equal to ∞, but multiplying a number (in this case, 2800) by another number (in this case, 3) an infinite number of times yields a value strictly greater than ∞. However, this subtlety is not properly picked up on in the anime, as Yami Yugi states that the ATK of "Legendary Knight Hermos" is ∞, and "Timaeus the Knight of Destiny" is destroyed by battle.
- Presumably, a maneuver like this would be the only way to destroy a Defense Position monster with ∞ DEF by battle, by getting a monster whose ATK is higher than that DEF.