Typical rules don't apply, for example:
Numbers with huge, hard to follow definitions: Allowed
Uncomputables, any order: Allowed
Infinities, Transfinites, any other kind of nonfinities: Allowed
Nonstandard Math: Allowed
Infinite Loops, Circular references: Allowed
Ill definitions, Undefined numbers: Allowed
External References, References to a dream your cousin mumbled about shortly before he passed out drunk: Allowed
Salad numbers, Naive Extensions: Allowed
Your number failed to actually be bigger: Thats ok, still counts!
Rule 1: Your number has X+ preceding it, where X is the previous post, unless your number uses the previous number in some other way (You may use X to reference it, in other words, X in the current post is shorthand for the number of the previous post).
The XKCD illion is 103Y+3 where Y = The latest number posted in this thread.