The Digit "1" is in the Neither Category in Relation to Prime and Composite Numbers

OKay, this debate stemmed off a mini-debate that we had in math class. We were discussing prime and composite numbers, and my teacher told us that zero was special and was neither, and so the class argued for five minutes about whether one was in the neither category or the prime category.

We never reached a conclusion.

Anyway, I'll start my debate.

One is in the neither category of numbers instead of the prime category simply because to be a prime number the number in question must be divisible by one and itself only.

Well one's only divisible by one number, one. And, to back up that argument, I will point out that "and" means 'in addition to'.

Prove me wrong.

You say that one is in the category of neither prime nor composite. I believe it is prime. The number 1 is divisible by one and itself. Although itself and one are the same thing, the number IS in fact divisible by both, and therefore fits the requirments you have stated.

prime number-a positive integer that is not divisible without remainder by any integer except itself and 1.

The number 1 is divisible by itself. It is also divisible by one. Therefore, I believe it is a prime number.

"the number IS in fact divisible by both"

But both of the numbers are the same thing, therefore "they" are one, and as such "they" are not both and cannot be both, for "they" will always be one.

"and therefore fits the requirments you have stated."

But, in fact, it doesn't, for both of the numbers you have stated are the same thing, and are therefore one number in truth.

http://dictionary.reference.com... - "2. added to; plus: 2 and 2 are 4. "

This can simply be restated as "in addition to"

To have something "in additon to" another, those two things must be different.

Okay, since me opponent failed to respond within the time allotted, I shall restate my position upon the subject.

The number one is in the neither category in relation to prime and composite numbers. The reason being is simple: One is only one number, and therefore the statement "One and one" is invalid in cases relating to the same thing and number.

Prove me wrong.

"But both of the numbers are the same thing, therefore "they" are one, and as such "they" are not both and cannot be both, for "they" will always be one."

The number one is divisible by both one and itself. No matter whether or not the number one is noted as both or as one, it is in fact divisible by both, no matter if 'both' is the same number.

In the definition of and that you supplied, it says 'in addition to, also, etc'. The number one is divisible by itself, and also the number one.

The number one is divisible by both itself and the number one. Although both are the same, this does not qualify it to be placed in neither group.