1 = 2
1 = 2
Originally Posted by NeoCracker
Okay, do you remember infinity? There are an infinite number of numbers after the decimal. True, the number approaches 1 as it goes further into infinity, but to say they are equal is just ignorant. We round and assume for simplicity's sake, but they are not equal!
0.999999999999 !=
0.99999999999999999999999 !=
0.999999999999999999999999999999999999 !=
0.9999999999999999999999999999999999999999999999999999999 !=
0.9999999999999999999999999999999999999999999999999999999999999999999999999999999 !=
1
Those are all different numbers.
Oh gods, why? ಥ_ಥ
This is actually all irrelevant seeing as 1/3 and 0.3333... are two different numbers.
Rational number shows what happens when you add 1/3 and 2/3 together;
This makes no sense. It's not a "misunderstanding," it's adding together rational numbers.
1 / 3 + 2 / 3 = (1 * 3) + (3 * 2) / (3 * 3) = 3 + 6 / 9 = 9 / 9 = 1
In case I wasn't clear this is what I mean; in any given situation involving an infinite series of decimal numbers, it's not possible to give an accurate answer to any kind of function performed on the number, especially when doing so with another infinite series, because the series are infinite. It's possible to solve this expression via the above fractions because we are dealing with a finite set of values.
Probably a bit of cognitive dissonance on my part, especially since I was working around the analogy of a number line. Technically speaking within the realms of real numbers, 0.999... is equal to 1. But this is done on the basis that Infinite isn't just a concept but a tangible, mathematical reality. I was attempting to rationalize why for example in the real world you can't cut a pie into three pieces and lose an infinitely small fraction of the pie. Then again we are talking about a profession that could probably prove the Universe doesn't exist technically, and which I only have a bare bones understanding thereof.This is also wrong, and I'm not even sure where you got this. It is a basic rule of algebra that any two, distinct real numbers have an infinite number of other distinct, real numbers between them. 0.999... is a real number.
There is no signature here. Move along.
you use the limit definition. You don't just use 'okay, 1/0=∞' or if you do, I'm sure your teacher marks you offYet we constantly use it in other proofsInfinity is not a finite, real number.
Because you are giving us finite numbers, numbers that have a distinct end. .9... is infinite; it goes on forever, and thus, you can't determine its end. Think of addition, which side to you start from when you want to add numbers? The right? But there is no right end in an infinite number.
Has anyone here (who is wrong) ever considered that we can have different looking numbers that represent the same thing? 1/2 == 4/8. No one has a problem with those once they have the knowledge. .9... and 1 are just another part of the stable of identical numbers; it's no different, you just need higher level math to prove it. Ohh, and there's plenty of proofs.
As I see it, all of this can be blamed on the awesome that is Calculus. Not only does it screw with minds, but it screws with lives and creates unnecessary DORAMA. .9... == 1, though. Just use the "can you find a number in between them" proof. There's also a proof involving limits and Taylor series, but I cba to find my math notes.
I was using finite numbers to show that they are not the same, that there are always infinately more 9's to add.
Oh gods, why? ಥ_ಥ
Hell, I learned this In my trigonometry class.
And a number that goes on infinately is not irattional, just impractical to use.
There is no real practical use to knowing 1 = 0.999..., but that doesn't change the fact that it does.
And PG made 2 of those threads? WTF?
Edit: Neotifa, you can't add a 9 to the end of something that has no end. So in this case, there are not always 9's to add to the end, proving your argument false.
You do know that the "..." already makes that assumption, right? There's no need for you to do it for us, because it would be impossible to show by spamming 9s.
Do you even know what the concept of infinite means?
0 < 1
Just use the ones place.
But being infinite means it isn't something you can parallel with finite numbers. 0.999... doesn't mean a lot of 9's and then you can add a few more to make a number between 0.999... and 1. It means that go on forever and there is no end, ever. At all. There is nowhere you can put another 9 on the end of because it has no end.
I know that 0.999... = 1 looks counterintuitive. I get that. The first time I saw it was scoffed at the obvious nonsense. But it is true despite the fact that it looks weird to the uninitiated.
Let's do this thread again, but in base 3.
Ughh, what the smurf ever. You're not understanding what I'm saying. Whatever. Suck it.
Oh gods, why? ಥ_ಥ
I love arguments like this.
A: *something*
B: *logical contradiction to thing*
A: WHATEVA
@rubah: 0.222... = 1
EDITGA<sup>2</sup>: Being able to argue in this thread first requires a firm background in Calculus and what 0.999... ACTUALLY MEANS. If you don't have this, you're doing it wrong and should probably just stop trying now.
Last edited by Denmark; 07-19-2009 at 08:23 PM.
Like I said before, disprove it's false. That is the only way to fully prove it is true.
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