Poll: 0.999... = 1
- Thread starter quhouv vhqwiufv qwiu
- Start date
Recommended Videos
x = 0.9999999999 (a finite number of 9s, for proof of concept purposes [or you can use infinity])crudus said:
10x = 9.999999999 (this is one less 9 than the number of 9s in x [or infinity - 1])
So the 10x - x would actually equal 8.9999999991, not 9. [or 8.(infinity - 1 nines)1] And no, that fraction shouldn't theoretically explode because the extra 1 on the end is the decimal place provided by subtracting 1 from infinity (providing you can do that, and in my brain, yes you can).
He multiplied by 10 thus shifting the decimal place over to the right one space. X had infinity decimal places and 10x has infinity - 1 decimal places. The infinite decimal places applies to x, not to the polynomial 10x. At least that's how I see it, the answer to the entire question relies on how you work with infinity...Rubashov said:
How about this one:
The difference between 0.9999.... and 1.0 is 0.0000... and since the difference between them is 0, the two numbers must be equal.
The difference between 0.9999.... and 1.0 is 0.0000... and since the difference between them is 0, the two numbers must be equal.
Well your poll is broken, but if it weren't I would point out that math isn't about opinions. The concept of infinity can get complex sometimes in math, it doesn't always mean exactly the same thing. If there's a proof for it, and it doesn't violate any rules like that one on the t-shirt on the first page, then that's the way it is.
True enough, but I still maintain that regardless of mathematical nonsense, this stands as a logic puzzle. .9(infinite) and 1 are not the same number because they are notated differently and therefore must be different, no matter how immeasurable that amount may be. But they can be treated as the same number BECAUSE that amount is so tiny, it wouldn't affect anything in practical use.crudus said:
Except you really aren't taking into account the <a href=http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel>Hilbert's Hotel concept that the proof relies on. Although, both point is moot. The proof seems to rely on the proof being true to be true.zfactor said:
Oh god, not this thread again.
Yes, it's fun to boggle the minds of people who don't understand higher math, but do we really need to do this again? It's just going to end up as another 100 page thread of people who don't understand the concept arguing with the people who do, and nothing is ever resolved.
Yes, it's fun to boggle the minds of people who don't understand higher math, but do we really need to do this again? It's just going to end up as another 100 page thread of people who don't understand the concept arguing with the people who do, and nothing is ever resolved.
But isn't math begging the question by default?crudus said:
Eh. Maybe not. But for all it's inherent logic, Math in the end still comes down to it's axioms. And those axioms are completely arbitrary.
They have to be, because if you can logically derive them, then you can decompose them into a combination of other parts that logically lead to them.
Therefore, the most fundamental axioms cannot themselves be logical statements, or you would have a infinite regression.
Fundamental problem with logic all round to be honest.
Logic, fundamentally, isn't logical. XD
I want to go with this, cause I dont know how i would disprove it.havass said:
But I would say no unless it says round up, simply cause no two numbers can be the same.
God damnit, I'm getting sucked into this, but I can't let this one slide. Two numbers that are notated differently are not automatically different numbers.enriel said:
3/6 = .5
Same. Number.
.999... = 3/3 = 1
Still. Same. Number.
But... Isn't infinity - 1 = infinity?zfactor said:
It's not even a different class of infinity, so that doesn't really help any.
Whenever infinity is invoked in anything, the results are difficult to interpret.
Suffice to say, if: infinity - 1 = infinity, then x and 10x in this case both have the same number of decimal places.
It's only if: infinity - 1 =/= infinity, that the example holds as it's being explained.
Erm, what?BlacklightVirus said:
I was saying .9999[infinity] is not 1 because they are not the same number: one is made up of bagillions of 9s and the other is a 1. Only same numbers can be set equal to each other, they are not the same number, they cannot be set equal to each other.
I was trying to use logic and avoid math... -sigh-
Let's say a_1 is .9; a_2 is .99; a_3 is .999; ... ; a_x is .[x nines].
The limit of a_x as x => infinity is, indeed, 1. However, a_[infinty] does not equal 1. The value is still .9999[infinity]. a_x will never equal 1. You can round it to equal 1, but it still will never be exactly 1...
This is actually a question related to calculus.
You'd be better off not describing X as X=0.9999999999999...
but rather X -> 1
which is to say, X approaches infinatly close to the value of 1, without ever actually becoming 1.
Treated algebraically, your proof is indeed correct, But as we can see, it ultimately fails the sanity test. Saying 0.999999999999=1 is ridiculous.
So in order to truly deal with the question, one requires a working knowledge of the fundamental principals of calculus.
You'd be better off not describing X as X=0.9999999999999...
but rather X -> 1
which is to say, X approaches infinatly close to the value of 1, without ever actually becoming 1.
Treated algebraically, your proof is indeed correct, But as we can see, it ultimately fails the sanity test. Saying 0.999999999999=1 is ridiculous.
So in order to truly deal with the question, one requires a working knowledge of the fundamental principals of calculus.