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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

 Messages: [ Previous | Next ]
 jsavard@ecn.ab.ca Posts: 403 Registered: 12/12/04
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 1, 2017 11:22 PM

On Sunday, October 1, 2017 at 1:22:43 AM UTC-6, netzweltler wrote:

> Do you agree that 0.999... means infinitely many commands
> ??
> 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.

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. 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