Arithmetic begins with counting, which in its simplist form is the repetitive adding of the number one. The next important operation is adding two single digit numbers. The number of possible ways to add the two single digit number totals 81 and these can be best represented in the form of a table. There are two traditional forms of addition tables. First is the following listing of the possible operations:
1+1 = 2
1+2 = 3
1+3 = 4
…
9+9 = 18
This presentation is complete and orderly, but very redundant: notice the repetition of the “+” and “=” signs and the repetition of the digits. A more efficient table is the two dimensional array that follows:
| + |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
| 1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| 2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
| 3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
| 4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
| 5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
| 6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
| 7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
| 8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
| 9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
