netzweltler
Posts:
473
From:
Germany
Registered:
8/6/10


Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
Posted:
Oct 2, 2017 1:58 PM


Am Montag, 2. Oktober 2017 17:59:21 UTC+2 schrieb Jim Burns: > On 10/1/2017 3:22 AM, netzweltler wrote: > > > Do you agree that 0.999... means infinitely many commands > > Add 0.9 + 0.09 > > Add 0.99 + 0.009 > > Add 0.999 + 0.0009 > > ...? > > 0.999... does not mean infinitely many commands.
But that's exactly what it means. Infinitely many commands. Infinitely many additions. Infinitely many steps trying to reach a point on the number line.
> There is a set of results of certain finite sums, a set of > numbers. We can informally write that set as > { 0.9, 0.99, 0.999, ... } > That is an infinite set, but we can give it a finite description. > > (Our finite description won't use '...'. The meaning of > '...' depends upon it being obvious. If we are discussing > what '...' means, it must not be obvious, so we ought to > avoid using '...') > > There is number which is the unique least upper bound of that set. > The least upper bound is a finite description of that number. > > 0.999... means "the least upper bound of the set > { 0.9, 0.99, 0.999, ... }". > That number can be show to be 1, by reasoning in a finite manner > from these finite descriptions of what we mean. > > If you give 0.999... some meaning other than what we mean, > and then it turns out there are problems of some sort with > your meaning, than that is your problem, not ours.

