Identity Property of Addition
Identity property of addition:
` 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.