It doesn't work because that poses the question:Originally Posted by Pureghetto
Let x = 1/∞
What is x/2?
There is always a less positive number for any k in R.
It doesn't work because that poses the question:
Let x = 1/∞
What is x/2?
There is always a less positive number for any k in R.
Ok, what number can you fit in between 0.999... and 1?
Easy .999.... + .999... Er, at least, I might as well say so!
It is like asking what whole number can you fit between 4 and 5. None, they are equal. There is something, as has been mathematically backed by brains far more simple than my own () which prove their is another finite layer that numbers do not correctly represent
Last edited by bipper; 05-22-2007 at 09:11 PM.
I didn't say whole numbers... I suck at math but the average of two different numbers fits in between those numbers. For example, 4 and 5's average is 4.5 and that fits in between 4 and 5. I'm fairly sure any value you can scrummage up to fit there would in fact have 21 chromosomes.Easy .999.... + .999... Er, at least, I might as well say so!
It is like asking what whole number can you fit between 4 and 5. None, they are equal. There is something, as has been mathematically backed by brains far more simple than my own (
There are no integers between two integers whose difference is 1. However there are always a real number between two different real numbers. That's how you tell numbers apart.
If 0.999... and 1 were different numbers I could subtract 0.999... from 1 and I would get a number. What is this number? It must exist if the two numbers were different.
Interesting how there's no such thing as a smallest number. I guess that Planck's constant and Planck-time and other Planck stuff do not apply to number theory :)
Uhm... Yes, Planck's.. whatever you just said!
I agree. Yep. Numbers.
The answer to that would be:
except that 0.000...1 is inherently impossible because the zeros go on forever. That's why the real numbers are flawed.Code:1 - 0.999... = 0.000...1
Get me a quantum computer and I might be able to give you the actual answer to that question.
Get a life and use a calculator. .
It's actually kind of simple I mean it's like if you had a dog, if you plucked one of his it's hairs that would no longer be a dog, merely a value that gets arbitrarily close to being a dog.
Show me a calculator that can calculate the difference between 0.999... and 1 and I'll gladly use it.
Um, or you realise that since 0.00000....1 doesn't make sense, you acknowledge that 0.999.... == 1 ?The answer to that would be:
except that 0.000...1 is inherently impossible because the zeros go on forever. That's why the real numbers are flawed.Code:1 - 0.999... = 0.000...1
Get me a quantum computer and I might be able to give you the actual answer to that question. :p
ok, just to put an end to this: 0.999... and 1 are the SAME NUMBER, there is no doubting it, ask the smartest person in the world and he or she will tell you that. scroll back up to my previous post and there is a WHOLE page there that explains everything...bottom line is: there is no use arguing, its a fact...so get over it: they are the same number...ok?
The best part of the ignorant masses who scream that .99999-... does not equal 1 are the ones who took one course in Calculus and try to prove it using limits, despite that the proof that .9999... = 1 is limits in Calculus. They say "limits get closer and closer to a number...." No, "x" in limit equations gets closer asnd closer to a number, but the limit is one number.
I don't remember the limit proof of this problem (I saw Dr Unne post it once - bug him), but a simpler example is lim x->infinity (1/x). This reads, for people who don't know calculus, as "the limit, as x approaches infinity, of 1/x." The answer is 0. As x gets bigger and bigger, closer and closer to infinity, the limit actually becomes 0. Not "closer and closer, but never reaching" 0 as the pseudo-intellectuals in this case want you to believe of .9999... and 1.
The easiest way to demonstrate the fact that .999... = 1 is the fact that there is no number between the two. Not only does any two distinct, real numbers have a number between them, but any two distinct, real numbers have an <i>infinite</i> amount of numbers between them. You can't even name one between .999... and 1, though, because there isn't any. The two numbers are equal.
Didn't Blizzard make an announcement on their main page about .999... = 1 a while ago? I seem to remember reading that.
Last edited by Raistlin; 05-23-2007 at 03:46 PM.
Yes.
As I said a couple of posts back, they're different representations of the same number under the equality operator in the real numbers.
Note, however that this holds under operations defined in the real numbers and complex numbers. If there exists a set where infinity or the concept of infinity can be treated as a normal entity then 0.999... could be shown to be inequal to 1.
Hmm, this doesn't have to be looked at through vector calculus.
0.999... = 9(1/10) + 9(1/10)^2 + 9(1/10)^3 + 9(1/10)^4 + ...
That sum is an infinite geometric series, and since the absolute value of it's common ratio is less than 1, it converges. So, you can calculate it's sum. It's involves a lot of Reimann sum symbols and other things that would involve annoying use of the character map, but it boils down to this:
ar + ar^2 + ar^3 + ... = ar/(1-r)
9(1/10) + 9(1/10)^2 + 9(1/10)^3 + ... = 9(1/10)/(1-(1/10)) = 1
So, 0.999... = 1. People can argue someone proving that with limits and say something about the nature of limits to infinity and their thoughts on infinitesimals, but the convergence don't lie.
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