infinite life vs infinite damage

[Guevara59]

My friend and i played a game in which i had infinite life and Marquise (my friend) was doing infinite damge...who wins??? Or is it a draw??? 

[Machinus]

If you gain "infinite life" first, and then they deal "infinite damage" second, then they win.

However, if there is some kind of instant speed war going on with priority, the rule is that whenever a decision has to be made about a certain number of loops or something, you have to pick a number. Then the opponent can pick a bigger one.

[andrewpate]

Machinus is correct.  See, you can't actually have infinite numbers in Magic, except with Mox Lotus.  When you gained "infinite" life, for example with Nomads en-Kor + Daru Spiritualist + Worthy Cause, you actually had to specify the number of times you were going to target the Spiritualist with the Nomads, which could be a very large number (say, a centillion), but which nonetheless must be a finite number.  So regardless of the amount of life gained, when the opponent deals "infinite" damage, for example with Rath's Edge + Wasteland + Glacial Chasm + Crucible of Worlds + Fastbond, he can always choose to activate the Edge one additional time in excess of the amount of life you gained.

So, in short, the most recent "infinity" always wins, because its controller can set it as high as necessary.