Liste des Groupes | Revenir à c theory |
On 3/27/24 8:56 PM, wij wrote:On Tue, 2024-03-26 at 22:17 -0400, Richard Damon wrote:On 3/26/24 10:45 AM, wij wrote:Snipet from https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber-en.txt/download
...
Real Nunmber(ℝ)::= {x| x is represented by n-ary <fixed_point_number>, the
digits may be infinitely long }
Note: This definition implies that repeating decimals are irrational number.
Let's list a common magic proof in the way as a brief explanation:
(1) x= 0.999...
(2) 10x= 9+x // 10x= 9.999...
(3) 9x=9
(4) x=1
Ans: There is no axiom or theorem to prove (1) => (2).
Note: If the steps of converting a number x to <fixed_point_number> is not
finite, x is not a ratio of two integers, because the following
statement is always true: ∀x,a∈ℚ, x-a∈ℚ
---End of quote
So, if 10 * 0.999... isn't 9.999... what is it?
and if 9 + 0.999... isnt 9.999... what is it?
And why aren't the same numbers the same numbers.
So, either your "wij-Reals" just fail to have the normal mathematical
operations defined or you have a problem with the proof.
Numbers defined with no rules on how to manipulate them are fairly
worthless.
The update was available:
https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber-en.txt/download
Hope, it can solve your doubt.
But the name "Real" is still very bad.
Particularly since you seem to say that any number that can't be
expressed in a finite number of digits in SOME base, is not a number in
your system,
since they can not be explicitly defined, OR HAVE MATH DONE
ON THEM, since
0.9999.... * 10 = 9. and somethnig not defined after it. (it isn't even
.999...)
So, your system seems more to be just the rationals. and you don't seem
to provide a clear set of axioms of what you allow to be done with these
numbers.
Les messages affichés proviennent d'usenet.