Re: [math-fun] More 4th grade math
Yes, 0 is the ultimate composite number. The use of the phrase "characteristic zero" is merely a hack, and nothing should be read into this usage. Once again, the primary reason for considering these 'corner cases' is to reduce the number of 'special cases' in definitions and proofs. In many cases, a formula can be extended to include the case n=0 or p=1 if the appropriate extended definition is used. It is easy to handle some of these definitions with "for all x in A, E(x)", so long as you realize that this works even when A is the empty set. Unfortunately, many speakers of English assume that when you talk about such an x, you seem to imply that such an x actually exists. At 06:26 AM 2/10/2014, Andy Latto wrote:
Do the people who say that 1 is a prime also say that 0 is a composite?
Wikipedia implies that the characteristic of a ring R (with unity) can be defined as the unique nonnegative integer such that nZ is the kernel of the ring homomorphism h:Z -> R (with h(1) = 1). Any field is also a ring, so this can be applied, making characteristic 0 a non-hack. --Dan On 2014-02-10, at 6:41 AM, Henry Baker wrote:
Yes, 0 is the ultimate composite number. The use of the phrase "characteristic zero" is merely a hack, and nothing should be read into this usage.
A bit of combinatorial trivia: you can define a multiplication on matrices of natural numbers using gcd for multiplication and lcm for addition. The identity matrix has zeros on the diagonal and ones off the diagonal. On Mon, Feb 10, 2014 at 11:16 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Wikipedia implies that the characteristic of a ring R (with unity) can be defined as the unique nonnegative integer such that nZ is the kernel of the ring homomorphism h:Z -> R (with h(1) = 1). Any field is also a ring, so this can be applied, making characteristic 0 a non-hack.
--Dan
On 2014-02-10, at 6:41 AM, Henry Baker wrote:
Yes, 0 is the ultimate composite number. The use of the phrase "characteristic zero" is merely a hack, and nothing should be read into this usage.
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