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Date |
10/06/97 at 12:47:29
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From |
Doctor Rob
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Subject |
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Re: The number 1 and zero
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One is neither a prime nor a composite number. A prime number is one
with exactly two positive divisors, itself and one. One has only one
positive divisor. It cannot be written as a product of two factors,
neither of which is itself, so one is also not composite. It falls
in a class of numbers called units. These are the numbers whose
reciprocals are also whole numbers.
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Zero is not a prime or a composite number either. Zero has an infinite
number of divisors (any nonzero whole number divides zero). It cannot
be written as a product of two factors, neither of which is itself, so
zero is also not composite. It falls in a class of numbers called
zero-divisors. These are numbers such that, when multiplied by some
nonzero number, the product is zero.
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The most important fact of multiplication of integers is called the
Fundamental Theorem of Arithmetic. It says that every whole number
greater than one can be written *uniquely* (except for their order) as
the product of prime numbers. This is so important that we tailor our
idea of what a prime number is to make it true. If 1 were a prime
number, this would be false, since, for example,
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7 = 1*7 = 1*1*7 = 1*1*1*7 = ...,
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and the uniqueness would fail.
