• 1.4: Inverse Property of Addition

    The inverse property of addition states that every real number has a special companion that we call its additive inverse. We define this additive inverse in relation to our additive identity, 0. Basically, the sum of a number and its additive equals 0, or the additive inverse of a number and its negative is 0. The fact that 5+(-5)=0 tells us that the number -5 is the additive inverse of the number 5.

    Note that there are no additive inverses if we only use positive numbers (the natural numbers)! We must use the larger, richer collection of integers to use our new property.

    You can think about this inverse property as mathematical cancel culture, where we regard our additive identity, 0, as a do-nothing or neutral number. The existence of additive inverses simply tells us we can undo, neutralize, or cancel every number. We can undo or cancel 10 by adding -10; we can cancel -42 by adding -(-42)=42. Here is a fun question to ponder: What is the additive inverse of 0?