RE: [split] 0.999... equals 1
February 2, 2012 at 8:57 am
(This post was last modified: February 2, 2012 at 10:24 am by Categories+Sheaves.)
I'mma drop some links
See: Wikipeida or Ed Nelson's introduction to nonstandard analysis for systems of analysis where this sort of thing need not happen.
There systems do treat infinitesimals as genuine, nonzero quantities. Here we have that .999... ~= 1 i.e. they are infinitely close, but we do not insist that .999... = 1.
Now, I'm a big fan of the standard real numbers, and I strongly prefer using them to the other systems out there. But the other systems are still out there. We do get this equivalence of .999... and 1 once we accept all that business with cauchy sequences and epsilon-delta. But definitely not before then.
See: Wikipeida or Ed Nelson's introduction to nonstandard analysis for systems of analysis where this sort of thing need not happen.
There systems do treat infinitesimals as genuine, nonzero quantities. Here we have that .999... ~= 1 i.e. they are infinitely close, but we do not insist that .999... = 1.
Now, I'm a big fan of the standard real numbers, and I strongly prefer using them to the other systems out there. But the other systems are still out there. We do get this equivalence of .999... and 1 once we accept all that business with cauchy sequences and epsilon-delta. But definitely not before then.