huge color(purple)(a+0=a)

What does it mean?

It means, that addition of zero to the number will not change the number.

Indeed, suppose your first friend (let's call it Tom) gave you 3 apples, but your second friend (let's call it Jim) gave you nothing. So, you are left with 3 apples.

Using commutative property of addition, we can write that a+0=0+a.

Thus, huge color(purple)(a+0=0+a=a).

This is also true, if we subtract zero: a-0=a.

In fact, identity property is true for any real number.

Example 1. 3+0=3.

Example 2. (-sqrt(2))-0=-sqrt(2).

Example 3. 0+5/8=5/8.

Conclusion. Addition or subtraction of zero doesn't change things.