Re: [math-fun] Re: Number derivative
It's (or at least, one flavor of it) based on the product rule: for functions f(x) and g(x), (fg)' = f'g + fg'. So with numbers, (ab)' = a'b + ab'. It only holds for natural numbers, due to the fundamental theorem of arithmetic. One can show that 1' = 0, and p' = 1 for any prime p. Then, for example, 6' = (2x3)' = 2'x3 + 2x3' = 1x3 + 2x1 = 5. You can find more details here: Ufnarovski, V., "How to Differentiate a Number," Journal of Integer Sequences, vol 6, 2003. Kerry Mitchell -- lkmitch@att.net www.fractalus.com/kerry
--- Kerry Mitchell <lkmitch@att.net> wrote:
It's (or at least, one flavor of it) based on the product rule: for functions f(x) and g(x), (fg)' = f'g + fg'. So with numbers, (ab)' = a'b + ab'. It only holds for natural numbers, due to the fundamental theorem of arithmetic. One can show that 1' = 0, and p' = 1 for any prime p. Then, for example, 6' = (2x3)' = 2'x3 + 2x3' = 1x3 + 2x1 = 5.
You can find more details here: Ufnarovski, V., "How to Differentiate a Number," Journal of Integer Sequences, vol 6, 2003.
Kerry Mitchell -- lkmitch@att.net www.fractalus.com/kerry
Then we have 2' + 3' = 1 + 1 = 2, (2+3)' = 5' = 1. So ' is not linear. Does this notion lead to something further, or is it a dead end? Gene __________________________________ Do you Yahoo!? Yahoo! Mail - More reliable, more storage, less spam http://mail.yahoo.com
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