Re:Why isn't 1 a prime number?
by zamadatix on Sunday April 28, 2019 @10:55AM
(#19771411)
It's a good example just a poor rendition of the definition of the fundamental theorem of arithmetic. The proper definition includes "either prime or the product of primes". Many mathematical texts shorten this to "the product of one or more primes" which doesn't make much sense to me but if you take it as acceptable to use "product" with a single number then some shorten it even further to "the product of primes" (primes now representing "prime numbers" not "multiple primes") resulting in what you see in many places/this article.
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It does make sense in a mathematical context though. You might write something like
p_S = \prod_{x \in S} x
And then later find out that the set S contains one element. Or it might even be the empty set in which case you'd interpret the above as equal to 1. This makes it work that
p_{S union S'} = p_S p_S'
in all cases.