Lesson Three: In Which Nothing Happens

Suppose people are arriving at school in the morning, and we are keeping track of how many arrive each ten minutes. For a while life is good, people arrive and we are adding them to the total number of people at school. After a while however, school starts and the arrivals stop. We eventually need to add nothing to the number of people at school!

Zero:

If we want to add nothing to our total, it would be helpful to have a numerical representation of nothing. This is of course 0. Anything plus 0 remains the same. This means that 0+1=1, so, since adding one gives us the next number, we can think about 0 as being the number before 1.

Optional Tangent:

For some rather advanced reasons, which I may get to later, 0 is actually a more philosophically sound place to start our numbers than 1. However, 1 is the starting place that I chose for three reasons: the argument for 0 is advanced, but not complicated, and I want to keep things simple for now; if I remember correctly, math education starts with the positive numbers then introduces 0 and I think that is worthy of emulation and; it makes sense historically, giving nothing its own symbol is something that came after the other numbers.