According to wikipedia: functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state an
I think you're just using the term "state" in an unusual way. If you consider adding 1 and 1 to get 2 as being stateful, then you could say functional programming embraces state. But when most people say "state," they mean storing and changing values, such that calling a function might leave things different than before the function was called, and calling the function a second time with the same input might not have the same result.