Math from Words
Chapter Nine - Multiplication

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Definition - Integer p is incremented 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 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.

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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.

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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.

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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.

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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.

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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.

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