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 Initial values for hyper operations bo198214 Administrator Posts: 1,386 Threads: 90 Joined: Aug 2007 03/14/2008, 10:44 AM During the introduction of zeration we saw already that there are some inconsistencies with the initial values. The addition as the successor operation of the successor operation (I consider here a[0]x=x+1 according to the rule a[n+1](x+1)=a[n](a[n+1]x) ) differs in its initial value from all the higher operations: a [1] 1 = a + 1 a [2] 1 = a a [3] 1 = a a [4] 1 = a .... If we would choose a[1]1=a we would get a[1]x=a+(x-1) I see a quite similar phenomenon when considering a[3L]x, the lower super operation of exponentiation, defined by a[3L](x+1)=(a[3L]x)[3]a. If we chose the initial condition in the used to a[3L]1=a manner then we get a[3L]x=a^(a^(x-1)). Especially in comparision with the similarly wrong defined addition a[1]x=a+(x-1) I would prefer to be a[3L]x=a^a^x a[3L]1=a^a Then we had unified a[3L]1=a[3]a a[1]1=a[0]a So does anyone see a strictly describable pattern when to use a ** 1 = a and when to use a ** 1 = a * a, where * is the sub operation of **. « Next Oldest | Next Newest »

 Messages In This Thread Initial values for hyper operations - by bo198214 - 03/14/2008, 10:44 AM RE: Initial values for hyper operations - by GFR - 03/19/2008, 11:03 AM

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