[Sofa King]

"Without defining the number system you are using, such statements are false."

If you don't define your number system, then you're talking about base 10. That 10 means 1x10^1 + 0x10^0 is defined in our language, and if you don't specifically state that you're redefining it to mean 1x3^1 + 1x3^0, then 2 + 2 = 11 is wrong. Math books, calculators, and most programming languages work that way.

[MineralMan]

"If you don't define your number system, then you're talking about base 10. "

Not so. That is your assumption, and it is not accurate. If I am reading a book on programming, there will be a different assumption, depending on the type of computer being programmed.

The moment I write 2+2=11, everyone should know I'm in Base 3. If I write 2+2=10, then I'm in Base 4. In all bases from 5 up, 2+2=4.