The idea of numerals is illustrated below. The numbers from zero to nine are depicted as dominoes shaded in blue. Though the numbers are depicted below, numbers are imaginary (they don't exist in real life). I've never seen the number five walking in my neighborhood or any other number for that fact. In this respect math is different from other sciences than say, chemistry, where atoms can be reached out and touched or geology where the Earth can be walked upon. After the "imaginary" numerals depicted below some addition and multiplication terminology is defined in the context of real analysis.

 0 Zero 1 One 2 Two 3 Three 4 Four 5 Five 6 Six 7 Seven 8 Eight 9 Nine 10 Ten

Please use the following two equations to use the multiplication and addition definitions following:

$a + b = c$

$x \times y = z$

sum
the union of two or more numbers, $c$
the two or more numbers in union, $a, b$
product
the result of multiplication, $z$
factors
the numbers multiplied to form a product, $x,y$

The addition table is outlined below. Only the numerals from zero through nine used. I'm not sure how much of a practice this is still today, but when I was in grade school back in the early 1980s (Gen X'er here), we had to memorize the addition and multiplication tables from 0 to 12. I made it through Saint Peter and Paul without ever getting paddled for not having my homework or misconduct. Though I think I did get a 'C' in conduct one semester.

 + 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18

Below is the multiplication tables for the number zero through nine. I created the table with HTML and Math (not the 'new' math mind you). Math is easy. Math is fun.

 $\times$ 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 2 0 2 4 6 8 10 12 14 16 18 3 0 3 6 9 12 15 18 21 24 27 4 0 4 8 12 16 20 24 28 32 36 5 0 5 10 15 20 25 30 35 40 45 6 0 6 12 18 24 30 36 42 48 54 7 0 7 14 21 28 35 42 49 56 63 8 0 8 18 24 32 40 48 56 64 72 9 0 9 18 27 36 45 54 63 72 81

That summarizes this page on Mathematics. Feel free to check out any of my other blog posts on math, statistics, computer science or audiophile equipment.