[catnaroek]

In the study of rings and fields, one works with operations called “addition” and “multiplication”, typically written “+” and “*”, but which needn't have anything to do with number addition or multiplication. “Addition” and “multiplication” have identity elements called “0” and “1”, respectively, but again, they needn't have anything to do with the numbers 0 and 1.

And, in a field of characteristic 2, there's no notion of 2, since “1 + 1” is by definition “0”.

[gridspy]

Putting "The sky is black" as a title seems incorrect to me, even though the statement "The sky is black on the Moon" is true.

[catnaroek]

+, × (or ·), 0 and 1 are standard notation in algebra for an arbitrary ring's addition, multiplication, additive identity and multiplicative identity. In that context, 1 + 1 = 0 isn't automatically false. It's just a statement that holds in some rings (e.g., F_2), but not in others (e.g., Z).