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

Replies: 42   Last Post: Oct 9, 2017 11:53 AM

 Messages: [ Previous | Next ]
 FromTheRafters Posts: 248 Registered: 12/20/15
Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
Posted: Oct 3, 2017 12:15 PM

Jim Burns submitted this idea :
> On 10/3/2017 8:20 AM, FromTheRafters wrote:
>

>> But 0.999 repeating is a rational number, no need for repeating
>> decimals at all in the naturals. Repeating zeros is okay I guess,
>> but why use them in the naturals. In the rationals and reals,
>> repeating zeros are called 'terminating' decimal expansions and
>> the trailing zeros are elided.

>
> Infinite decimals represent real number "fractions".
> The need for 0.999..., such as it is, is for _some real number_
> to be assigned appropriately to every infinite decimal expansion.

I agree, if you meant infinite 'repeating' decimal expansions, but
netzweltler wrote about little n in N (n an element of the naturals)
and was using decimal expansions which aren't needed in whole numbers.
Sure, in the rationals and the reals decimal expansions certainly make
sense.

> It's the same reason we assign the infinite decimal 0.1234000...
> to the terminating decimal 0.1234. We want 0.1234000... to be
> _something_ . What else would it be?

I think you missed my point. Netzweltler should have had little r in R
or at least little q in Q to use decimal expansions to illustrate his
point. He should use real numbers to illustrate real number ideas. It
is plain to see that in the reals there are always other numbers
between any two other reals which are 'different' from each other due
to the density. The same works for irrationals (fractions) -- but not
so much for the naturals.

Why did he specify the naturals when he was trying to say something

Date Subject Author
10/2/17 Guest
10/2/17 netzweltler
10/2/17 Jim Burns
10/3/17 netzweltler
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 netzweltler
10/3/17 bursejan@gmail.com
10/4/17 netzweltler
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 netzweltler
10/3/17 Jim Burns
10/4/17 netzweltler
10/4/17 Jim Burns
10/4/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 FromTheRafters
10/6/17 netzweltler
10/6/17 Jim Burns
10/7/17 FromTheRafters
10/8/17 FromTheRafters
10/8/17 netzweltler
10/8/17 Jim Burns
10/8/17 netzweltler
10/8/17 Jim Burns
10/9/17 netzweltler
10/9/17 Jim Burns
10/9/17 netzweltler
10/9/17 Jim Burns
10/7/17 Jim Burns