 Logic hyperoperators - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Logic hyperoperators (/showthread.php?tid=1027) Logic hyperoperators - hixidom - 10/14/2015 Something that occurred to me recently (maybe it's already been mentioned here somewhere)... Say ab = a+b and ab = 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(ab) = a OR b and H(ab) = 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, %: (ab)%2 = a XOR b (ab)%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