Liste des Groupes | Revenir à c theory |
On Sat, 2024-03-30 at 10:01 -0400, Richard Damon wrote:What number does the representation 0.abc represent?On 3/30/24 9:56 AM, olcott wrote:You are nut who always think he is talking B while reading A. (x!=c)On 3/30/2024 7:10 AM, Fred. Zwarts wrote:>Op 30.mrt.2024 om 02:31 schreef olcott:>On 3/29/2024 8:21 PM, Keith Thompson wrote:>olcott <polcott2@gmail.com> writes:>On 3/29/2024 7:25 PM, Keith Thompson wrote:[...]>What he either doesn't understand, or pretends not to understand, isIn other words when one gets to the end of a never ending sequence
that the notation "0.999..." does not refer either to any element of
that sequence or to the entire sequence. It refers to the *limit* of
the sequence. The limit of the sequence happens not to be an
element of
the sequence, and it's exactly equal to 1.0.
>
(a contradiction) thenn (then and only then) they reach 1.0.
No.
>
You either don't understand, or are pretending not to understand, what
the limit of sequence is. I'm not offering to explain it to you.
>
I know (or at least knew) what limits are from my college calculus 40
years ago. If anyone or anything in any way says that 0.999... equals
1.0 then they <are> saying what happens at the end of a never ending
sequence and this is a contradiction.
>
It is clear that olcott does not understand limits, because he is
changing the meaning of the words and the symbols. Limits are not
talking about what happens at the end of a sequence. It seems it has
to be spelled out for him, otherwise he will not understand.
>
0.999... Limits basically pretend that we reach the end of this infinite
sequence even though that it impossible, and says after we reach this
impossible end the value would be 1.0.
Nope. Shows you don't really understand what limits are.
>
And are just a pathological liar as you insist that you falsehoods based
on the wrong definitions are the truth.
>
https://www.geneseo.edu/~aguilar/public/notes/Real-Analysis-HTML/ch4-limits.html
Limit is defined on existing numbers, it cannot define the the number it is using.
Things is very simple: "repeating decimal" means the pattern is infinite.
(you are worse than olcott in this)
If it does not exit, your math (repeating decimal is ...) is garbage talking
about something does not exist and use it as proof of fact.
>>0.999... indicates the Cauchy sequence xn, where x1 = 9/10, x2 =>
99/100, x3 = 999/100, etc. The three dots indicates the limit n→∞. The
= symbol in the context of a limit means in this case:
For each rational ε > 0 (no matter how small) we can find a number N
{in this case 10log(1/ε)}, such that for all n > N the absolute value
of the difference between xn and 1.0 is less than ε.
It is not more and not less. Note that it does not speak of what
happens at the end of the sequence, or about completing the sequence.
If olcott wants to prove that 0.999... ≠ 1.0 (in the real number
system), then he has to specify a rational ε for which no such N can
be found. If he cannot do that, then he is not speaking about real
numbers.
>
Les messages affichés proviennent d'usenet.