What Type of Number Are Zero and One?
Date: 11/08/2004 at 20:27:37 From: Kay Subject: What are the numbers 1 and 0 classified as? If 1 and 0 are not considered prime or composite numbers, then what are they? This question was extra credit from school. 1 is not considered prime because it doesn't have only two factors, 1 and itself, and it's not composite because it doesn't have more than two factors. So what are they considered to be? I did see that 1 was called a unit (or that's what I understood) from the following discussion: http://mathforum.org/library/drmath/view/57058.html But I want to know what 0 is called and I would like a little clarification and a confirmation for this statement. Thanks!
Date: 11/10/2004 at 12:23:14 From: Doctor Roy Subject: Re: What are the numbers 1 and 0 classified as? Hi Kay, Thanks for writing to Dr. Math. When the Greeks first described prime numbers, they had a conception that the only "true" numbers were whole numbers (1,2,3,4,....) and later ratios of whole numbers (i.e. fractions). So, when they defined prime numbers, they meant positive numbers only. The current definition of a prime number is a positive integer greater than 1 (i.e. the counting numbers 2, 3, 4, 5, etc.) whose only divisors are 1 and itself. A composite number is a positive integer greater than 1 which is not prime. Zero is not positive, so it falls outside the prime/composite categorization. In fact, negative numbers are also neither prime nor composite. I think the underlying confusion lies in the idea that all numbers must be prime or composite. This is not true. It is only positive whole numbers greater than 1 which are either prime or composite. So, 0 and 1 fall outside prime/composite categorization. So do 1/2 and pi and -2 and many other numbers. An analogy which may help: We say that some mammals are lagomorphs (if it is a rabbit or a hare or a pika) or rodents. So, a mouse is a rodent and a hare is a lagomorph. Then what is an elephant? If it is not a lagomorph or a rodent, what is it? The answer is that it is neither. Mammals cannot simply be split into two groups by this classification. Specific mammals can, however, be split into these two groups. 1 and 0 are numbers which cannot be placed into the groups "prime" and "composite". There are several characterizations of numbers they fall into, but prime and composite are not among them. If you think about it, there are several other categorizations: negative/non-negative negative, zero, positive even/odd divisible by 6/not divisible by 6 algebraic/transcendental Prime/composite just happens to be a particularly interesting one that applies only to certain numbers. Does this help? Please feel free to write back with any questions you may have. - Doctor Roy, The Math Forum http://mathforum.org/dr.math/
Date: 11/10/2004 at 22:36:42 From: Kay Subject: Thank you (What are the numbers 1 and 0 classified as?) Thank you very much Doctor Math! This reply has really made me think more about this. I did in fact get the same answer when I browsed the boards after I asked. This gave even more information. Thank you so much! - Kay
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