In article <PuQRj.587$Q97.511@[EMAIL PROTECTED]
>,
"Jim Langston" <tazmaster@[EMAIL PROTECTED]
> wrote:
> Storm wrote:
> > Please bear with me if I am not following a protocal for the group.
> >
> > My step daughter is in 9th grade math (she is in 7th grade).
> > She asked me earlier in the week if .999 going off in to infinity is
> > the same thing as 1.
> >
> > I said no. Close...but no.
> > I am by far no pro at math.
> > She insists its the same, because her math teacher said so...
> >
> > But, I do seem to remember a math teacher telling me that
> > mathmatically, it can be the same as one. In reality it is not. He
> > told me to think of two lines. To be parallel, the need to be the
> > same distance apart...say 1. If they are .999999 apart...eventually
> > they will meet. And, no matter how far out you go in to infinity,
> > you still will not reach 1. Best I can think of is that this is a
> > mathmatical concept, that
> > exists on paper....
> > Can anyone here give an answer that makes sense to me, or her?
> > Thanks....
>
> I'm a programmer and some new programmers have a hard time with floating
> point numbers. Take, for example, the decimal number 0.1 In binary it
is
> .000110011... with the 0011 repeating forever. It can not be accureatly
> represented in binary.
It is accurately represented as a binary expansion, just not a finite
one.
> There are some numbers in decimal that are the same. Such as 1/3 which
we
> write as 0.33333... We can not accurately write them in decimal.
Sure you can, just not as a finite decimal expansion.
> 0.9999999.... is one such number which comes from adding 1/3 three
times.
> 0.33333333.. + 0.333333.. + 0.33333333... = 0.99999999999...
>
> Yet we know that 1/3 + 1/3 + 1/3 = 1.
>
> 0.999999... doesn't really exist in nature,
It exists just fine. Perhaps you would like to tell us what "exist in
nature" means.
> just as 0.333333... doesn't
> exist in nature, it is our mathematical system, the way we humans came
up
> with a numbering system, it is not perfect. And because 0.99999999.. is
not
> an accurate representation of the number we need to realize that the
> accurate representation is 1.0.
>
> Lets see how to convert 0.99999999 to a fraction.
>
> x = 0.9999999999
> 10x = 9.9999999999
> Right? So what is 9x? 10x - x
> 9x = 9
> divide both sides by 9
> (9x) / 9 = 9 / 9
> x = 1
That argument doesn't make sense unless you know what .9999... means.
And if you have given meaning to it, you already know it = 1.
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