Re: Repeating decimals are irrational

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 */