Strange! Before James and I posted one could read the following text below Jerkey’s last post, although he was the last one who posted (before James and me):
“Last edited by jerkey on Wed Jun 29, 2016 5:24 pm, edited 2 times in total.”
Yes. Therefore all this operations have to do with the infinitesimal calculus (inveted by Gottfried Wilhelm Leibniz). So James is right with his answer.
James, you’re treating an infinite string as though it’s just a really, really long finite string (thus leaving a “last little bit”, presumably after the “last digit” at the “end” of the “endless” string…). That isn’t true. A really, really long finite string has a last digit, an infinite string does not. A really,really long finite string would indeed leave a “last little bit” left over, but we aren’t talking about a really, really long finite string, we’re talking about an infinite string. That distinction is crucially important.
No. That is what YOU are doing when you claim that there is a 0 “at the end once it gets to infinity”.
I am saying that because there is no end, the 9s must still be going - ALWAYS (true by definition). And thus never, ever becoming the string of 0s required for “1.000…”.
In Your response ending in ‘that clould never happen’ -5 of Your responses back in the forum, and the one two back, ending with ‘impossible’ - referring to machine intelligence.
It could never happen - is equivocal to - impossible
The claim is that there are two decimal expansions for the number 1: a 1 with an infinite string of 0s after the decimal, and 0 with an infinite string of 9s after the decimal. Both are equivalent decimal expansions for the same integer. So there is no requirement that the 9s morph into a string of 0s, the string of 9s itself is equal to 1.
Multiple forms of the same value are common in math: 1/2 = 2/4 = 3/6 = 0.5 = .4999…
Jerkey, he simply means that the equation of 1 = 0,999… does at last not absolutely work: although the difference of both numbers becomes smaller and smaller, they can’t become equal, because there remains always a rest, an infinite small rest but a rest. So this equation works mathematically, of course, but that does not mean that it also works logically, thus philosophically. It is a solution for mathematicians but not for philosophers. One can always say that there is a rest that denies the equation.
This also indicates that mathematics and philosophy are two different disciplines, and history has shown that they have to be different disciplines.
That is your false assertion that you keep claiming, yet haven’t provided any proof at all, whereas I have provided two proofs that you have yet to fault, but rather merely deny.
True, because you keep misstating it. Most recently, you claimed that for .999… to equal 1, at some point in the decimal expansion the 9s have to be replaced with 0s. That isn’t true, it not required, it’s not what anyone’s claiming. That claim is that .999… and 1 are equivalent decimal expansions of the same integer.
You accept that the limit as the number of 9s goes to infinity is 1, right?