An important addition to the number line is the number 0, which means nothing, zilch, nada. Step back a moment and consider the bizarre concept of nothing. For one thing — as more than one philosopher has pointed out — by definition, nothing doesn’t exist! Yet, we routinely label it with the number 0, as shown in the following figure.
Actually, mathematicians have an even more precise labeling of nothing than zero. It’s called the empty set, which is sort of the mathematical version of a box containing nothing.
Nothing sure is a heavy trip to lay on little kids, but they don’t seem to mind. They understand quickly that when you have three toy trucks and someone else takes away all three of them, you’re left with zero trucks. That is, 3 – 3 = 0. Or, placing this on the number line, 3 – 3 means start at 3 and go down 3, as shown in the above figure.