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Topic: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Replies: 31   Last Post: Oct 3, 2017 3:02 AM

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 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 3:12 AM

Am Montag, 2. Oktober 2017 05:22:32 UTC+2 schrieb Quadibloc:
> On Sunday, October 1, 2017 at 1:22:43 AM UTC-6, 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
> > ??
> > Then following all of these infinitely many commands won?t get you to point
> > 1. If you reached point 1 you have disobeyed those commands, because every
> > single of those infinitely many commands tells you to get closer to 1 but
> > NOT reach 1.

>
> You would be correct if Zeno's paradoxes were correct. But they're not.
> Achilles can and does overtake the tortoise every day.
>
> 0.9999... does *NOT* mean actually doing those infinitely many steps. There
> is never time to do that many commands. Instead, it means the place that
> doing them would take you, if you _could_ do them.
>
> Yes, doing any _finite_ number of those commands would not get you to 1. You
> would have to disobey them to get that far.

Even doing an _infinite_ number of those commands wouldn't get you to 1.

1. 0.99 + 0
2. 0.99 + 0
3. 0.99 + 0
...

Neither a finite number of the steps on the list above will get you to 1 nor an infinite number of the steps on the list above will get you to 1. We can tell that - no matter if we can do all the steps or not. For each particular line is true that we don't reach 1. And this is true for this list also:

1. 0.9 + 0.09
2. 0.99 + 0.009
3. 0.999 + 0.0009
...

> But you *can't* do an infinite number of commands. Period.
>
> So that isn't the criterion you use to figure out what 0.9999... actually
> is.
>
> Is 0.9999... not equal to 1? In order for it _not_ to be equal to 1, it
> would have to be less than 1 by some finite number.

Why that? 0.999... cannot be located at point 1 of the number line. Why do you think that means that it must be short of 1 then? It cannot be located at a point < 1 either.

> But pick any such
> number, and by doing a sufficiently large finite number of commands, you can
> get closer to 1 than that.
>
> So 1 is indeed the only thing it can be equal to, even though that looks
> funny. But that's just a problem with the decimal system of writing numbers
> - it doesn't perfectly match the real numbers it refers to - not with the
> numbers themselves. It doesn't mean infinitesimals have to be added to the
> real number line.
>
> John Savard

Date Subject Author
9/30/17 mitchrae3323@gmail.com
9/30/17 netzweltler
9/30/17 FromTheRafters
9/30/17 mitchrae3323@gmail.com
10/1/17 netzweltler
10/1/17 mitchrae3323@gmail.com
10/1/17 jsavard@ecn.ab.ca
10/1/17 mitchrae3323@gmail.com
10/2/17 netzweltler
10/2/17 Jim Burns
10/2/17 netzweltler
10/1/17 FromTheRafters
10/1/17 netzweltler
10/1/17 FromTheRafters
10/1/17 netzweltler
10/1/17 FromTheRafters
10/2/17 netzweltler
10/2/17 FromTheRafters
10/2/17 netzweltler
10/2/17 FromTheRafters
10/2/17 netzweltler
10/2/17 bursejan@gmail.com
10/2/17 Me
10/2/17 netzweltler
10/2/17 bursejan@gmail.com
10/2/17 bursejan@gmail.com
10/2/17 bursejan@gmail.com
10/3/17 netzweltler
10/2/17 FromTheRafters
10/2/17 jsavard@ecn.ab.ca
10/2/17 netzweltler