>>14
That's not what I meant. Those who believe that 1 is different from 0.999... can only admit the difference is an infinitesimal. If we integrated using that infinitesimal, what would be get?
>>13
see >>17
Anyhow, I dunno how a theoretical mathemetician would handle this, but it's my undertanding that if there were an infinite amount of 9's there, then this would simply approximate 0, and so it could be treated as zero within a certain number of decimal places.
and you... >>12
wouldn't infinitely small pieces be very little? I think they would.
>>21
So what you're saying is if you change the base from say 10 to 2, then you end up with a whole other interesting problem. So once again we have to look at what the numbers are being used for. In general 0.9999999... approximates 1, however under special circumstances it may not be adequate, so what are those circumstances exactly, and there you would have a problem that Calculus probably couldn't solve. Thanks for pointing that out.