EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 06:46 PM |
So suppose you add 1 + 2 + 4 + 8 and so on. Each number being twice as big as the previous one.
But we can multiply the whole thing by 1.
1 * x = x
So...
1 + 2 + 4 + 8 + 16 + ... = 1(1 + 2 + 4 + 8 + 16 + ...)
Right?
And 1 = (2 - 1)
So we can do this:
1 + 2 + 4 + 8 + 16 + ... = (2 -1)(1 + 2 + 4 + 8 + 16 + ...)
So we have...
... ... ... ... ... = 2 + 4 + 8 + 16 + ... ... ... ... ... ... = -1 - 2 - 4 - 8 - 16 - ...
So... Almost everything on the right side cancels itself...
1 + 2 + 4 + 8 + 16 + ... = -1
Meaning adding infinity results in -1. |
|
|
| Report Abuse |
|
|
dekkonot
|
  |
| Joined: 22 Dec 2010 |
| Total Posts: 6685 |
|
| |
|
xSIXx
|
  |
| Joined: 06 Aug 2010 |
| Total Posts: 9202 |
|
| |
|
LocalChum
|
  |
| Joined: 04 Mar 2011 |
| Total Posts: 6906 |
|
| |
|
elucidir
|
  |
| Joined: 08 Aug 2011 |
| Total Posts: 243 |
|
|
| 21 Aug 2011 06:51 PM |
| You left out the last term in the positive sequence. |
|
|
| Report Abuse |
|
|
EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 06:52 PM |
| ^ Nope make the math and you'll se why the 1 isn't there anymore. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 06:52 PM |
Why do noobs think that infinity is a number? Was it on a cartoon or something?
Infinity is NOT a number, it is a concept. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 06:53 PM |
| You're doing it wrong. Just letting you know. |
|
|
| Report Abuse |
|
|
elucidir
|
  |
| Joined: 08 Aug 2011 |
| Total Posts: 243 |
|
|
| 21 Aug 2011 06:53 PM |
The last term.
On the right side. (It's 32) |
|
|
| Report Abuse |
|
|
EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 06:55 PM |
@Arceus
Who said infinity is a number?
I'm saying that using that algorithm to sum numbers ends up on -1. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 06:56 PM |
| It doesn't. Subtraction of infinity from infinity is undefined. |
|
|
| Report Abuse |
|
|
EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 06:56 PM |
| It isn`t a last term it's infinity, the ... means the sequence continues indefinitely. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 06:56 PM |
"Who said infinity is a number?"
You implied that it was. How do you add past something that isn't a number? |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 06:58 PM |
You have done it wrong, notably, once you reach the line "1 + 2 + 4 + 8 + 16 + ... = (2 -1)(1 + 2 + 4 + 8 + 16 + ...)" you start to make mistakes. This is how you would do the math:
...... = (2)(1 + 2 + 4 + 8 + 16...) + (-1)(1 + 2 + 4 + 8 + 16)
You would not assume them equal to each other, you'd do it that way. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 06:58 PM |
| The sequence 1 + 2 + 4 ... tends to infinity. So does the sequence 2 + 4 + 6 ... However, you're assuming that you can subtract these two sequences and get a valid result; you can't. |
|
|
| Report Abuse |
|
|
EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 06:59 PM |
| That is how you'd do the math not how you present it. For obvious reasons I used a compound multiplication instead of writing the whole thing. |
|
|
| Report Abuse |
|
|
EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 07:01 PM |
| @fungal Actually they are just the same sequence but after the multiplication. I separated them into two sequences for easier reading and explanation. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 07:02 PM |
You still did it wrong. I'll redo it for you in a correct way that makes complete and logical sense:
So suppose you add 1 + 2 + 4 + 8 and so on. Each number being twice as big as the previous one.
But we can multiply the whole thing by 1.
1 * x = x
So...
1 + 2 + 4 + 8 + 16 + ... = 1(1 + 2 + 4 + 8 + 16 + ...)
Right?
And 1 = (2 - 1)
So we can do this:
1 + 2 + 4 + 8 + 16 + ... = (2 -1)(1 + 2 + 4 + 8 + 16 + ...)
So we have...
2 + 4 + 8 + 16 + ... = (2)(2 + 4 + 8 + 16 + ...) + (-1)(2 + 4 + 8 + 16 + ...)
Using simple math...
2 + 4 + 8 + 16 + ... = 2 + 4 + 8 + 16 + ...
You're trying to represent it in a way that you just logically shouldn't in math, so you come to an invalid result. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 07:04 PM |
Your assumption was that the series, when it was subtracted itself, equaled zero. That is not the case.
1 + 2 + 4 + 8... - 1 + 2 + 4 + 8... is undefined. |
|
|
| Report Abuse |
|
|
EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 07:04 PM |
| ^ Actually what you did there is wrong. Let me rewrite hat last part. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 07:06 PM |
"Actually what you did there is wrong. Let me rewrite hat last part."
No it was not :V I passed my Algebra classes with flying colors, I know my mathematical properties pretty well. You're trying to represent it invalidly, so you're coming to a bad result. |
|
|
| Report Abuse |
|
|
EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 07:06 PM |
1 + 2 + 4 + 8 + 16 + ... = (2 -1)(1 + 2 + 4 + 8 + 16 + ...)
So we have...
1 + 2 + 4 + 8 + 16 + ... = (2)(1 + 2 + 4 + 8 + 16 + ...) + (-1)(1 + 2 + 4 + 8 + 16 + ...)
Adding it all results in:
1 + 2 + 4 + 8 + 16 + ... = 2 + 4 + 8 + 16 + 32 + ... + -(1 + 2 + 4 + 8 + 16 + ...)
Meaning that if you add up everything in those 2 sequences end up in -1. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 07:07 PM |
| Lolwhoops I said Algebra and not mathematics :V Probably because I was thinking of Algebra and how I have Algebra II next year :V |
|
|
| Report Abuse |
|
|
EaglEyeX
|
  |
| Joined: 18 Jun 2008 |
| Total Posts: 1193 |
|
|
| 21 Aug 2011 07:07 PM |
| And this is totally valid math. Probably not what you are shown at your age but it is. |
|
|
| Report Abuse |
|
|
|
| 21 Aug 2011 07:09 PM |
1 + 2 + 4 + 8 + 16 + ... = 2 + 4 + 8 + 16 + 32 + ... + -(1 + 2 + 4 + 8 + 16 + ...)
is false. Adding an series that sums to infinity, with one that sums to negative infinity, does not give you a valid result. It's undefined. |
|
|
| Report Abuse |
|
|