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| 26 Feb 2012 04:40 PM |
Eh, last time everybody said it rounded up, because of infinite 9.9999999.... wel,, it's still a decimal, and if you wanna be exact, you don't round it up, even though that would be useful, and you can't do anything with infinity, because it never ends... (inf-1=???????), and since infinity does not represent a number, but is a mathmatical term to represent NEVER ENDING or ALWAYS TRUE or ON, you can't solve it within an infinite amount of time, minus 1 from infinity. If you got that, you're a boss.
-This was INFINITELY cool... how to explain infinitely cool? uh...- |
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| 26 Feb 2012 04:44 PM |
"you don't round it up"
Yes, you do, because it is exactly the same as one.
x=0.999... 10x=9.999... 10x-x=9.999...-0.999... 9x=9 x=1
Congratulations, mathematical proof. You say you can't do anything with infinity, but luckily for us, this isn't infinity. This is an infinitely repeating decimal, which is different. You can perform operations on infinitely repeating things, but you cannot perform operations on infinity itself. |
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| 26 Feb 2012 04:46 PM |
Infinite infinite of an infinite=??? still, I see your point.
-KITTIES- |
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1Ra
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| Joined: 02 May 2010 |
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| 26 Feb 2012 04:46 PM |
Think of infinity as a fast growing line, 1 - infinity would just be a line moving 1 pace behind infinity. therefore, infinity*2 = a line growing twice as fast as infinity.
thats how i think of infinity. |
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| 26 Feb 2012 04:47 PM |
| Derp, I did the previous proof wrong, I thought you said 0.999... and not 9.999..., but just multiply everything on the right by 10 and you get the same proof. |
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| 26 Feb 2012 04:49 PM |
| @1Ra, infinity can't be doubled because it can't equal anything, because infinity never ends... yeah, no subtracting 1 or multiplying by 2... |
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| 26 Feb 2012 04:52 PM |
"Think of infinity as a fast growing line, 1 - infinity would just be a line moving 1 pace behind infinity. therefore, infinity*2 = a line growing twice as fast as infinity.
thats how i think of infinity."
Technically speaking, you're thinking of it wrong. Infinity is a concept of something that never ends, and it has no numerical value. Operations cannot be performed on it because our nicely defined numerical operations end up with erratic and disputed behavior when you try to incorporate infinity. There are times where it's useful to define certain operations with infinity to have a constant result, such as any division by infinity resulting in 0, but in my opinion those types of definitions are more limited to calculus concepts, such as limits. |
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| 26 Feb 2012 05:01 PM |
| Basically, scientists didn't know how to define never ending and said it was "infinity". |
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Oysi
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Varp
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| 26 Feb 2012 05:25 PM |
Sure you can work with infinite numbers! Consider Hilbert's paradox of the Grand Hotel (which deals with the size of the set of natural numbers):
There is a hotel. Its rooms are numbered 1, 2, 3, and so on. This hotel, as a matter of fact, has an infinite number of rooms! Each room has a guest within it.
Say another guest arrives. Every room is occupied, but this guest can still be accommodated. How? Well, just ask everyone to move to the room with a number 1 higher. The person in room 1 goes to room 2, the person in room 2 goes to room 3, etc.. This allows our new guest to go to room 1!
While this can be expressed formally, doesn't that show that if you take an infinite number, then add one, it has not changed? |
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Oysi
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Varp
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| 26 Feb 2012 05:41 PM |
"Which is obviously false, so that proves infinity can't be treated as a number."
0*x = 0*y
Should we stop treating 0 like a number as well? I'll just cut out a little slit in my number line to accomodate your argument. 0 definitely is a number, but how do we accomodate this problem? Well, we say that it's illegal to divide by 0. What you'd really be doing to get from the above statement to a contradiction is:
Let f(x) = 0*x = 0 f(x) = f(y)
This is true, but after this step is where we went wrong. Suppose that there is some function, g, that is the inverse of f:
f(g(x)) = x 0 = x
That's a contradiction, therefore f(x) = 0 has no inverse. We cannot continue the proof, but no contradiction can be reached.
Infinity can be used in a similar way. We note that:
f(x) = x*infinity = infinity (for x >= 0)
So we have the same problem: we're trying to invert a constant function. In fact, you can make a whole myriad of false arguments with constant functions!
If f(x) = 4, it follows that f(2) = f(3), but not that 2 = 3 |
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Oysi
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| 26 Feb 2012 05:48 PM |
| Technically, that would mean that, just like we aren't allowed to divide by zero, we shouldn't be allowed to add or substract infinity, nor to multiply by infinity, nor to divide infinity, not to do anything that has to do with infinity. |
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| 26 Feb 2012 05:49 PM |
"Excellent point. But what about inf + 1 = inf...
inf + 1 = inf"
No. Technically, it would mean that you just can't calculate inf + 1 and that it doesn't equal anything. It would mean that, just like you can't divide a number by zero, you can't add 1 to infinity. |
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Varp
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| Joined: 18 Nov 2009 |
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| 26 Feb 2012 06:01 PM |
"Technically, that would mean that, just like we aren't allowed to divide by zero, we shouldn't be allowed to add or substract infinity, nor to multiply by infinity, nor to divide infinity, not to do anything that has to do with infinity."
Why can't we add infinity to a finite number? That doesn't lead to contradictions. Why can't we add infinity to infinity (of the same sign)? Why not multiply and divide by non-zero, finite numbers?
These things all lead to constant functions of the form:
Let f(x) be _(verb)_ing x and infinity. f(x) = infinity
So, yeah, they're not at all invertible, but that just means that inverting them is illegal, not that they themselves are illegal. If you're working with the cardinal numbers, as a matter of fact, you can PROVE that N = N + 1.
You're blaming the victim! It's not infinity's fault that you're manipulating it wrong! |
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Quenty
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| 26 Feb 2012 06:18 PM |
The crazy thing is different sized infinities.
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| 26 Feb 2012 06:25 PM |
" Basically, scientists didn't know how to define never ending and said it was "infinity". "
No, they did know how to define it, and called it "infinity". If you have a number that is infinitely small(such as 1/infinity), it is negligible. Just like how 0.9999999 is basically 1 - 1/infinity, it will just round up to 1. Why would anybody possibly want to work with an infinite amount of significant figures? |
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| 26 Feb 2012 06:27 PM |
| Note: the "0.9999999" in my previous post is continued infinitely, like you have mentioned earlier. |
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lah30303
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| 26 Feb 2012 07:18 PM |
| lol, I leave roblox for 2 years and come back and people are still talking about infinity like it's going to help them cure cancer. |
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1waffle1
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| 26 Feb 2012 07:52 PM |
"people are still talking about infinity like it's going to help them cure cancer." That's how much money research is going to cost, so why not talk about it a little?
One problem that I have with infinity is the idea that there are just as many numbers between 1 and 2 as there are between 1 and 3. There are obviously twice as many numbers between 1 and 3 than there are between 1 and 2. Since this deals with numbers, though, then it makes sense that it doesn't make sense, since infinity is not a number. |
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| 26 Feb 2012 08:00 PM |
@1waffle1
It makes perfect sense that there is the same number of numbers between 1 and 2 as there is between 1 and 3.
~+[CROOKITY BANDED SNAKES]+~ |
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fox1238
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| 26 Feb 2012 09:32 PM |
| X+r=t. X= 5(9+14) r =x -31 |
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fox1238
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Varp
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| 26 Feb 2012 09:54 PM |
"One problem that I have with infinity is the idea that there are just as many numbers between 1 and 2 as there are between 1 and 3. There are obviously twice as many numbers between 1 and 3 than there are between 1 and 2. Since this deals with numbers, though, then it makes sense that it doesn't make sense, since infinity is not a number."
Pssh, that's not at all worrying. There are as many numbers between 0 and 1 as there are real numbers; Consider the bijective function:
f(x) = tan(x*pi)
It maps numbers in the range [0,1] to ALL real numbers, so those sets have the same size. That's a little troubling. Worse still, there are as many real numbers as there are 2D vectors (or 3D vectors). The easiest way to prove that is to take the binary representations of both numbers in the vector, and splice them together (first bit is of the x coordinate, second is the y coordinate, then x, then y, x, y, etc.). That gives you a real number which is unique.
So, there as many numbers between 0 and 1 as there are vectors in 10 dimensions. Math is worrying. |
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