How can 1 plus 1 equal 3?

Answer 1

If you use base three then 1 + 1 = 3, as the current counting system we use is base ten

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Not true. 1 + 1 does not equal 1 in base 3, it equals 2.

010 = 03

110 = 13

210 = 23

310 = 103

410 = 113

You can get 1 + 1 = 3 if you redefine the operator "plus".