Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.theory
Subject: Re: Repeating decimals are irrational
Date: Tue, 26 Mar 2024 17:28:32 -0700
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wij <wyniijj5@gmail.com> writes:
> On Tue, 2024-03-26 at 17:01 -0700, Keith Thompson wrote:
>> wij <wyniijj5@gmail.com> writes:
>> > On Tue, 2024-03-26 at 16:22 -0700, Keith Thompson wrote:
>> > > wij <wyniijj5@gmail.com> writes:
>> > > > On Tue, 2024-03-26 at 15:55 -0700, Keith Thompson wrote:
>> > > [...]
>> > > > > Do you understand what a mathematical limit is?  Can you explain it?
>> > > > > 
>> > > > > If you understand limits, you should be able to understand that
>> > > > > 0.333..., where the "..." denotes the limit as the number of 3s exceeds
>> > > > > without bound, is exactly equal to 1/3.
>> > > > > 
>> > > > > [...]
>> > > > > 
>> > > > 
>> > > > I already stated it the file:
>> > > > https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber-en.txt/download
>> > > 
>> > > OK, in that file you wrote:
>> > > 
>> > >     Ex1: A= lim(n->∞) 1-1/n= lim(n->0⁺) 1-n= lim 0.999...=1
>> > >          B= lim(n->∞) 1+1/n= lim(n->0⁺) 1+n= lim 1.000..?=1
>> > > 
>> > > What do you mean by that question mark?  Do you agree that both limits
>> > > in your example (A and B) are equal to 1?
>> > > 
>> > 
>> > Agree.
>> 
>> OK.  Do you agree that 0.333..., where ... denotes the limit as the
>> number of 3s increases without bound, is exactly equal to 1/3?
>> 
>
> Nop.

I'll assume that's a typo for "No" or "Nope".

So you're saying that 0.333... is not exactly equal to 1/3.

It seems odd that you agree that 0.999... is exactly equal to 1, but
0.333... is not exactly equal to 1/3.

Is 0.333... a real number?  Is 1/3 - 0.333... a real number?  What is
the value of 1/3 - 0.333...?

>> And that that number multipled by 3 is exactly equal to 1?
>> 
>> And that 0.999... is exactly equal to 1?
>> 
>> And that all the numbers we're discussing are both real and rational?
>
> Can you make statement really like math?

Please rephrase that.  I don't understand what it means.

> You still keep asserting your belief, not a proof but strangely formed statement !!!
> You cannot read proof !!! Go home and learn more.

I haven't offered a proof because (a) there's no point in doing so if we
don't have enough mutual understanding, and (b) I'm not a mathematician,
so I'm not confident of my ability to construct a rigorous proof.  I
might give it a try later, but I see no point in doing so now.

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
void Void(void) { Void(); } /* The recursive call of the void */