Math from Words

Chapter Nine - Multiplication

by

W is the set of whole numbers.

M is the set of non-positive numbers.

If p is in W, and q is next in order from p, inW, then p becomes q.

If q is a negative number in M, and p is next in order from q, in M, then p becomes q.

-----------------------------------------------

**Definition** - *Integer p is decremented* if and only if each following statement is true:

W is the set of whole numbers.

M is the set of non-positive numbers.

If q is a positive number in W, and p is next in order from q, inW, then p becomes q.

If p is an integer in M, and q is next in order from p, in M, then p becomes q.

-----------------------------------------------

**Definition** - *Integer p is changed by integer q* if and only if the integer sum of p and q is the integer which p becomes now.

**Definition** - *Positive number C is the product of positive number A and positive number B* if and only if C is q when the following is done:

AA. k is 0.

BB. q is 0.

CC. The whole number in W next in order from k is the number that k becomes now.

DD. The sum of q and B is the number that q becomes now.

EE. If k is A then q is the product of A and B, and this procedure is done.

FF. Go to CC.

-----------------------------------------------

**Definition** - *Positive number C is the product of positive number A and negative number B* if and only if C is q when the following is done:

AA. k is 0.

BB. q is 0.

CC. The whole number in W next in order from k is the number that k becomes now.

DD. The integer sum of q and B is the number that q becomes now.

EE. If k is A then q is the product of A and B, and this procedure is done.

FF. Go to CC.

-----------------------------------------------

**Definition** - *Positive number C is the product of negative number A and positive number B* if and only if C is q when the following is done:

AA. k is 0.

BB. q is 0.

CC. The whole number in W next in order from k is the number that k becomes now.

DD. The integer sum of q and A is the number that q becomes now.

EE. If k is B then q is the product of A and B, and this procedure is done.

FF. Go to CC.

-----------------------------------------------

**Definition** - *Positive number C is the product of negative number A and negative number B* if and only if C is q when the following is done:

AA. k is 0.

BB. q is 0.

CC. The whole number in W next in order from k is the number that k becomes now.

DD. The integer sum of q and |A| is the number that q becomes now.

EE. If k is |B| then q is the product of A and B, and this procedure is done.

FF. Go to CC.

-----------------------------------------------

**Definition** - *X is raised to the N* if and only if each following statement is true:

X is an integer.

N is a whole number.

X raised to the N is notated this way: X^{N}.

If N = 0, then X^{N} = 1.

If N = 1, then X^{N} = X.

If N = 2, then X^{N} = X(X).

For any integer X, and any whole number N > 0, X^{N} is the product of N numbers that each equal x.

-----------------------------------------------

**Download**