Forgive me, since I assume you know this...
Define your number set as base 2 := {0,1,2}
Then 1+1=2, yet 2+2 =22, etc.
I was being facetious.
That came from the time when my kids were little and we were talking about math and how a child reasons, and when you ask them what 2 and 2 equaled, that they were just as likely to answer 22 as 4, simply because they misunderstood the question.
Like when you’re explaining how to read two digit numbers. A 1 and a 2 is twelve. So a 2 and a 2 would be 22. So when you asked what 2+2 was, the answer could be 22.
Good grief, get it right.
Base 2 uses only the digits 0 and 1, it’s also called binary and used in computers. What we write as 2 is represented as 10.
(Hence the computer nerd shirt inscription: “There are 10 kinds of people, those who understand binary and those who don’t.”)
If you use base 3, you have the digits 0, 1 and 2, then 2 + 2 = 11, not 22.