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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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: XN.
If N = 0, then XN = 1.
If N = 1, then XN = X.
If N = 2, then XN = X(X).
For any integer X, and any whole number N > 0, XN is the product of N numbers that each equal x.
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