Thats right, "1+1=2" is not absolute because it depends on our definition of the basic arithmetic operations(addition, subtraction, multiplication, division). As these operations are usually defined 1+1 will result in 2, but if you choose a non-standart arithmetic system 1+1 could not result in 2 anymore. There are many non-standart arithmetic systems. People find so hard to believe that "1+1=2" is not absolute, but that is basic knowledge, any mathematician will agree with that.
Standart arithmetics have four or maybe eight axioms(I don´t remember exactly) which are statements that are assumed to be true without being proved. One of these axioms says that "x+0 = x". You can define a non-standart arithmetic where "x+0 = 0", and you can do that. Its not contradictory to do that, it is just a different arithmetics. In an arithmetic system like this you can prove that 1 + 1 = 0, like: 1+1 = (1+0)+(1+0) = 0+0 = 0
1+1=2 is not an absolute because it depends on the definition of the operation addition that we are using. The operation addition is not absolute. It is the way it is because someone choose to define it in that way.