One way that 1 + 1 could not "equal" 2 would be if you changed the basis of the number system. One would typically think that the numbers were on the base-10 system meaning that 1 + 1 = 2.
But, if one were to using a base-2 system, then 1 + 1 = 10 .
Technically, it still equals 2 (base-10), but is now written as 10 (base-2), i.e., 210 = 102 .
Hope this answers your question.