How 0 plus x equals x?

Answer 1

0 is the identity under addition for integers, rationals, reals, complex numbers. This means that 0+x = x+0 = x for all x.

The above answer is correct, but with some mild "un0carefulness" as we call 0 the identity BEAUSE 0 + x = x + 0 = x for all x in those sets.

As a matter of fact, we want something in our sets with an operation to be the identity, we just decided to call it 0.

In other words, we DEFINE 0 as a element in a group, ring, field, or other number systems where 0 + x = x + 0 = x for all x.

By the way, if you don't like it, you can call it something else. Like @ + x = x + @ = x for all x. You just have to define it. Then you can use it on your papers :P After all, 0 without a definition is just a symbol.