It could be 4. Over C, R, Q and Z it is. So in that kind of "mathematics" that is actually taught in schools.

It also could be 0 over Z(2) = Z / Z(2) := { z from Z | z mod 2 [ from {0,1} ]} . A field .

It also could be 1 over Z(3) = Z / Z(3) := { z from Z | z mod 3 [ from {0,1,2} ]}. Another field .

It also could be 4 over Z(p) = Z / Z(p) := { z from Z | z mod p [ from {0,1,...,p-1} ] | p prime unequal to 2, 3} . A field.

It also could be 5 over Z_(5/4) := { z from Z | 5/4 * z } . A ring as Z itself is. The most trivial example to show you how powerful definitions can be.

Obviously these are all nontrivial solutions to this equations.

I just defined this to open up your minds for other definitions.

These are just some of the possibilities.

Be careful though with this. Mathematics knows almost no limits here.

So you can conclude from this that it depends on the field or ring you are actually doing calculations in what the result of this equation is.

That is why real mathematicians always define the field or ring in addition to the equation they are solving these equations in.

Homework (for the nerds or those that want to become nerds) :

a) Define a ring such that 2 + 2 = z with any arbitrary z (a whole number) .

b) Extend this ring such that 2 + 2 = a / b with a and b relative prime with a and b from Z .

c) Prove or disprove if there exists a field in which 2 + 2 = 5.