There is also an argument that our notation is just limited for the proofs that 0.9999... = 1. For example, this proof does not hold if you change to a different base.
… in base 3, would be:
1/10 = 0.1
10*1/10 = 10 * 0.1
1 = 1
… or base 6,
1/3 = 0.2
3*1/3 = 3*0.2
1 = 1
That doesn’t necessarily answer you question about calculations that use limits, but I think the general answer is yes use the limit.
Okay, got it.
So, we can prove that 0.999… = 1 in other bases?
More that 0.999999… is an imprecise representation of the value.
0.9999… does not converge to 1 … IT IS 1.
This is actual ragebait
First of all, this man, the author of the article, is literally just a guy with free time, while sites like Wikipedia use actual, reliable sources that they show at the bottom. I scrolled to the bottom of this article and, what do you know, there are no sources, it’s literally just this one guy who is way overconfident. Also, almost every comment that I read was showing him how he is wrong. This is also his only math-related article, even though he claims that he has “disproven” many facts. Reminds me of a flat-earther.
Well I was getting all confused, cause Daniel is saying something about not converging.
Yes, I agree.
He knows nothing about what he is talking about. It is incorrect to say that 0.999… x 10 = 0.999…0. I don’t know how anyone thinks this is possible. First, it is very obvious that any “0” at the end of a number can be neglected.
Secondly, the “0” does not exist. You cannot have an digit after an infinite amount of digits. The “0” does not change the value of the decimal.
Another thingif, according to this logic, 0.999… * 10 = 0.999… 0 ,
then does 0.999… * 10 = 9.999… 00?
Then, does, 0.999… * 10^n = 0.999 * 10^n … (0)n?
So are you saying that 0.999… * 10 ^n = 0.999… 0…?
How do you even have “repeating 0s”? That doesn’t even make any sense! And we aren’t even taking in account, you are having repeating 0s AFTER repeating 9s!
Edit
From the third equation, 0.999… * 10^n = 0.999 * 10^n … (0)n, can be simplifed into:
0 = 0.00…
(cancelling out the 0.999… * 10^n)
Do you see the problem? What is a “0.00…”? Can you ignore those 0s? “No”, because they have some “infinitesimal” value that is absolutely nonexistent.
.999… is NOT 1 becuase is diferent looking actualy
Yes, and Daniel_Grubbs showed (smartly) that you can express 0.999… = 1 easily in different bases:
@bhssingul this is not targeted at you btw, don’t take this personally, it’s against your source
two numbers and argument = personal
Read though this and nearly had to correct everything I saw, but thankfully the incorrect and rage-bait was corrected.
I was crashing out when I saw 0.999… * 10 equaled 0.999…0. Just the concept of a repeating number and then another number out of sequence is impossible.
ok, let’s be precise then …
0.999 … and 1 are two ways to indicate
the same exact number.
Yes thank you Guzman
Just because a number “looks different” doesn’t mean it IS different. For example, 2/2 sure looks different from 1. Same value, different representation.
No, he meant:
“0.999… is not equal to 1 just because they look different”
I assume
Nothing personal @bhssingul , but this is absolutely nonsensical.
I was being sarcastic
Oh. My bad. I struggle with picking up sarcasm through text.
mmm ok so 4 and 8 are the same number too