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That convention is only stated as a "law" on wikipedia and in areas of set theory that are used by non-Mathematicians -- and you'll notice that when it's stated it's always termed using the set of "natural" numbers, where no-one can agree whether or not zero is a member of the set.
So prime numbers are a subset, which may or may not include one, of a subset of all numbers that may or may not include zero? How very precise and mathematical.
It's one of those "Oh, did you know..." non-factual conventions that get bandied around, based on the real fact that it is sometimes necessary to exclude one from the set (e.g. to use the arithmetic sieve of Eratosthenes -- which is about as far as most proponents of the "law" can go with Maths).
Us Mathematicians don't need half-educated prats fannying around in our field. If calculations require the inclusion of one as part of a set of primes, then it's included, and the same goes for zero and natural numbers -- include what's needed, don't include everything else, but don't bother anyone with spurious "laws" based on the requirements of a subset of all calculations.
A little learning, as always, is a dangerous thing -- but it's precisely what wikipedia is made of.
Surely based on the Euclidian definition it is not a prime as it is not factorable?
Looks like it can be factored to me, and that's just using integers and no rounding -- 1*(0.5 recurring)=1, to whatever number of decimal places you decide to use.
Dalek Dave wrote:
And anyway, isn't it a special case as it is a unit?
One is not a unit, one is a number (or, linguistically, a numerical determiner).
The "unit" is an abstract item equal to one of something, which means that it can be any number of anything, e.g. when working with quarters, four is the unit known as the denominator, and 100 is one of the units commonly used when working with percentages (which is why some idiots try to declare that you can't have more than 100% -- they can't see that after "one something" comes "more than one somethings").
That one is the number most commonly used as a unit in basic integer arithmetic doesn't mean that it is a unit; it is sometimes used as a unit, just as it is sometimes included as a prime.
You cannot set a "law" stating that it is always either, because it isn't -- it's 100th of the percentage unit 100, for example, and four quaternary units (to achieve 1, you need four quaternary units in the numerator if four is the denominator).
The only actual law is that one is not another number, but that same law is true for all numbers.
I wanna be a eunuchs developer! Pass me a bread knife!