Addition builds on Counting. It is faster and easier to see a pile of 3 and a pile of 5 and think 3+5=8 than it is to count from 1 to 8. People unconsciously learn additions, such as “three and five is eight” without trying. At some point a person would notice what was being done, and that person might decide to formalize Addition.
By Formalize, we mean, take the time to think about, talk about it, and discuss it (possibly with Beer involved) with friends.
Any value plus zero equals that value. This is a simple rule but it is valuable to us for it is one of the building blocks things to come…
Appendix A
When writing axioms, Peanu wrote two for Addition:
- a + 0 = a
- a + S(n) = S(a + n)
S(n) is the Successor Function.
S(1)=2
S(2)=3
At this point you’re probably thinking, oh, the successor is the next number.
From what we have above we can use a+0 to get a+1 and we then have a+2 and so on, thus we can add ‘a’ and any integer, in principle. In practical, you might not live long enough to get to ‘n’.
Rob Sterling 