What would happen if 1 plus 1 were not equal to 2?

Answer 1

"2" means "1 more than 1." So the only way that 1+1 would not equal 2 would be if "1" or "2" were defined in a way other than as we know them. For example, if "2" were defined as "2 more than 1", that is, 3, then 1+1=3, not 2, by definition. But then we would choose another symbol for "1 more than 1," which would really be 2, no matter what we called it. The important thing in mathematics is that all who communicate using a number set agree on each definition. But if you could suddenly, magically change the meaning of 2 to something else, without defining a new "1 more than 1" and obtaining everyone's agreement, we would be instantly beset by universal inconsistency. Mathematics would become useless. [Others might here contribute examples of what would go wrong.] Interesting note: In the binary number system, used internally by computers, there is no "2", only "0" and "1". In binary arithmetic, 1+1=10, where the 0 is in the 1s place and the 1 is in the 2s place. (1+1 is still 1 more than 1, but it is represented as "10".)