Printable View
If you subtract 0.999.... from 1 you get an infinitesimal value { x | x > 0 && x < { http://upload.wikimedia.org/math/6/9...41811fd226.png } }Quote:
Originally Posted by Raistlin
I'm not going to waste your time with limits and other crap. 0.999.. = 1 is an equation. I am disproving the equation by defining 0.999.. differently.
QED
If you define 0.999... differently then it's no longer 0.999.... If it's not a decimal followed by an infinite series of nines, then of course it doesn't equal one. You could redefine any number to equal whatever the hell you want it to. But with that definition, if you subtract it from 1, the answer is 0, and therefore they are equal.
nop I'm not defining 0.99... differently I'm saying 1 - 0.99... is infinitesimal QED asians!Quote:
Originally Posted by Raistlin
If by "infinitesimal" you mean "zero," then you are correct. Otherwise you are clearly and objectively wrong, and you know that because you're just an azn troll. Quod erat demonstrandum.
.9 repeated is not one. However, they both act as the same number unless pushed to extreme circumstances. For example .9 repeated raised to an infinite power would be 0, while 1 to the infinite power is an indeterminate form, and while it may be zero as well it must be dealt with on a case by case basis.
Here is my reasoning that .9 repeated to the infinite power converges to zero.
Given that k >= 0
If that n is a real number -1 < n < 1 and n =/= 0
Then nk > nk+1
The first 5 iterations of this with n =.5 are as follows.
.5, .25, .125, .0625, .03125 .....
A love math :quina:
I'm not a troll.Quote:
Originally Posted by Raistlin
And no I already defined infinitesimal as a real number that is less than all real numbers and greater than 0.
A real number minus a real number cannot be a non-real number, at least in our current number system. You can invent another one if you want.
This is where your assumption breaks down, because 0.999... is not less than 1. It is exactly 1, and you have not demonstrated otherwise. This has been firmly established for a long time. Raising it to an infinite power is no different than raising 1 to an infinite power.Quote:
Originally Posted by qwerty
The real question is, that if the two numbers are identical, and work indentically in every circumstance:
Why do people continue to use .999... when 1 is so much easier to type, and why does this discussion continue to pop up?
If those two symbols are proven to mean the same thing, then just use the simpler one. That's why we use Leibniz's notation instead of Newton's. The only reason you have to use .999... over 1 is because you are wanting to cause pointless discussion and commentary of the subject.
This is a remarkably pointless question. What do you mean "continue to use"? I'm pretty sure no one writes out "0.999..." instead of "1" when working on a basic problem. Of course, it can be the first answer reached in certain other problems. Why do people ever use 2/2 or 5/5 for 1? Or 0.3-bar instead of 1/3? Just because an answer can be "simplified" to a different symbol which means the same thing doesn't mean the original number is invalid. If you are using calculus working on an infinite series, or working with rational infinitely-repeating decimals, 0.999... may well be an answer you get to first before "reducing" it to 1 -- although the decimal or fraction form may be easier to work with in some of those calculations.Quote:
Originally Posted by Skyblade
And this discussion continually becomes up because some people are too irrational to accept something that goes against their initial knee-jerk reaction. And this can be entertaining for the rest of us.
.9 repeated is used in number theory.
Also Raistlin have you ever attempted to solve the birthday problem?
What is the smallest group of people required so that it is more likely than not that one person has the same birthday as another?
Dear Everyone Who Has Posted In This Thread; Past, Present, Future:
smurf you. Sincerely, a giant smurf you. I hope something terrible happens to you. However, I'm going to extend that desire to your entire family and circle of friendship as well. I hope a meteor made entire of :bou::bou::bou::bou:, dropped from a 747, bursts into your home while you are sleeping, dreaming of puppies and kittens, or some other cute :bou::bou::bou::bou:, and completely destroys everything you love and value. I hope, beyond hope itself, that a centaur magically appears out of some smurfing fairy tale, and violates you with it's giant human-horse dong. There is also a small desire that you lose a leg or two, in addition to your left arm and most of the fingers on your right hand, in an accident possibly involving a beaver. I sincerely wish this upon all of you dickbags for what travesties you have committed by being involved in this, or any form of this thread.
Triple Sincerely Yours (with love in my heart and a hate-fueled rifle in my hand),
Bunny von Trapp
P.S. Math sucks.
And here are the entertaining reactions I was speaking of. http://www.thegamersalliance.net/for...ilies/pimp.gif
Yes, I've heard of this probability problem, but it doesn't really have anything to do with this issue. Are you just posing it as another interesting math problem? I prefer the Monty Hall problem if I wanted to blow people's minds.Quote:
Originally Posted by qwerty
(SPOILER)You always switch doors.Quote:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
I hope this happens to me too :love:Quote:
Originally Posted by Bunny
Also hahahahaha the Monty Hall problem is going to make people rage, Wes.
To add to the 0.99.. thread here:
Please to tell me the value difference of the following numbers:
1
1.0
1.0000
1.000000
1.000000000000000000000000000000
1.000000000000000...
What do you mean they mean the same? BUT THEY ARE DIFFERENT NUMBERS LOSAFLSDJO ASL
I wasn't being facetious in the other thread but I am here.
I know, that's why I love it so much. Wikipedia says the magazine that first published it got thousands of letters saying how wrong it is. I hated statistics class for some of its largely arbitrary equations, but I love some of the counter-intuitiveness of probabilities.
EDIT: in response to MILF.