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Logic hyperoperators - hixidom - 10/14/2015
Something that occurred to me recently (maybe it's already been mentioned here somewhere)... Say a[1]b = a+b and a[2]b = ab, Then if "true" and "false" are defined as 1 and 0, respectively, and if a and b are restricted to boolean values, then H(a[1]b) = a OR b and H(a[2]b) = a AND b. where H(x) is Heaviside function with H(0)=0. So, by analogy, H(a[1.5]b) would be some sort of interpolant of AND and OR. Alternatively, you could use modulus operator, %: (a[1]b)%2 = a XOR b (a[2]b)%2 = a AND b therefore (a[1.5]b)%2 interpolates AND and XOR. Somehow I feel that the use of H and % corrupt the validity of this idea, but I'm just curious if anyone else can get further with this than I can. Thanks for reading. Andy |