> On 28 Jan., 12:41, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: >> I'm asking about a single number, 0.777..., which you >> claim is terminating. >> >> Please show that there is a k and f as required by the definition of >> terminating decimal representation so that > > By *your* definition of terminating, this may be required. Not by the > mathematical definition which relies upon the fact that every natural > number is finite and that a non-terminating decimal cannot be defined > by digits but only by the finite definition: "This decimal will never > end".
Well, you agreed to that definition.
> My definition of terminating says only that the terminating decimal > belongs to the set of all terminating decimals, which is as well > defined as the set of all natural numbers.
If you ask me for the definition of the set of natural numbers, I would be happy to provide it. Please, tell me your definition for the set of all terminating decimals and we may proceed.
> In order to show that a decimal is not terminating, you are obliged to > find a digit, the index of which doe not belong to a FISON (1, 2, ..., > n). Of course you will fail. But nevertheless try it. > > That are the rules.
I'll believe that are the rules only after I see the appropriate definition.
(If that are, indeed, the rules, it will follow that every real, including the square root of 2, Chaitin's omega ad so on, are terminating decimals, by the way. But we will wait to discuss that until after you provide a definition consistent with the rules.)
-- Jesse F. Hughes "But you have to support spyware if you're going to have free file-sharing applications. Fair's fair." -- NYU student Keith Caron in Wired