Infinity Elemental

• WWizards of the Coast2020-02-29
  Official Ruling
  If you give Infinity Elemental lifelink and it deals damage, you will gain infinite life. You might think infinite life sounds like a lot, and you’d be right. Once at infinite life, your life total mostly can’t change (see below). At infinite life and gain 2 life? You’re at infinite life. At infinite life and lose 29 life? You’re at infinite life. You can pay any amount of life and still be at infinite life. In fact, if you’re at infinite life and get with an opposing Infinity Elemental, you’d still be at infinite life.
• WWizards of the Coast2020-02-29
  Official Ruling
  If you’re at infinite life and attempt to draw a card from an empty library . . . you lose. You’re not immortal.
• WWizards of the Coast2020-02-29
  Official Ruling
  Infinity Elemental’s power is incalculable. Infinity Elemental has the greatest power among creatures on the battlefield (and off the battlefield for that matter), although it will tie with other Infinity Elementals. Gaining or losing power is meaningless to it, although effects that set its power to another number will still work.
• WWizards of the Coast2020-02-29
  Official Ruling
  If an effect sets your life total to a specific number, it will be that number, even if you previously had infinite life.
• WWizards of the Coast2020-02-29
  Official Ruling
  Through various other cards, you can convert the infinite power of Infinity Elemental into other resources. For example, you could have infinite mana or create infinite tokens. You could draw infinite cards, but that many card don’t exist, so it’s probably not a great idea. Forcing another player to draw infinite cards, on the other hand . . . .

Rulings via Scryfall