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mikesgt2
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#1
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#1
What is the sum of the infinte series:

1 - 1 + 1 - 1 + 1 - ...

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GH
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#2
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(Original post by mikesgt2)
What is the sum of the infinte series:

1 - 1 + 1 - 1 + 1 - ...

?
We can say that the sum is (1-1) + (1-1) + (1-1) + (1-1)...
Which of course (1-1)=0, so it is like saying 0+0+0+0+0....
which is 0.

BUT, we can also say that 1 + (-1+1) + (-1+1) + (-1+1)....which means that it would be 1+ 0 +0 + 0 + 0 + 0 + 0...which is 1.

Since both calculations give the same answer we can assume that 0 = 1.

However why 2 different answers? Well since infinity has no defined value then the question itself is fallicious, so the answer you get is fallicious.
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GH
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(Original post by 2776)
We can say that the sum is (1-1) + (1-1) + (1-1) + (1-1)...
Which of course (1-1)=0, so it is like saying 0+0+0+0+0....
which is 0.

BUT, we can also say that 1 + (-1+1) + (-1+1) + (-1+1)....which means that it would be 1+ 0 +0 + 0 + 0 + 0 + 0...which is 1.

Since both calculations give the same answer we can assume that 0 = 1.

However why 2 different answers? Well since infinity has no defined value then the question itself is fallicious, so the answer you get is fallicious.
Anyone agree with me?
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chrisbphd
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(Original post by 2776)
Anyone agree with me?
Yes. Spot on.
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elpaw
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(Original post by 2776)
Anyone agree with me?
did you read that in the New Scientist issue about infinity?
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Ralfskini
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(Original post by elpaw)
did you read that in the New Scientist issue about infinity?
I read the article today, about an hour ago.
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Ditzy
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(Original post by Ralfskini)
I read the article today, about an hour ago.
Is it in the latest issue?
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elpaw
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(Original post by ditzy blonde)
Is it in the latest issue?
no it was from early october i think, cant remember exactly
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mikesgt2
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(Original post by 2776)
We can say that the sum is (1-1) + (1-1) + (1-1) + (1-1)...
Which of course (1-1)=0, so it is like saying 0+0+0+0+0....
which is 0.

BUT, we can also say that 1 + (-1+1) + (-1+1) + (-1+1)....which means that it would be 1+ 0 +0 + 0 + 0 + 0 + 0...which is 1.

Since both calculations give the same answer we can assume that 0 = 1.

However why 2 different answers? Well since infinity has no defined value then the question itself is fallicious, so the answer you get is fallicious.
Yup, I agree. But there is another possibility:

Let the sum of the series be x

We can say that: x = 1 - x
=> 2x = 1
x = 1/2

I think you could also argue that x = -1/2

This was just an interesting thing I found in a book about infinity.
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a_musical_git
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A baby could have worked that sum out! I don't know, Maths these days is getting easier and easier.
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Ralfskini
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(Original post by elpaw)
no it was from early october i think, cant remember exactly
27th September. I'm a little behind.
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elpaw
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(Original post by Ralfskini)
27th September. I'm a little behind.
your clock is running faster than mine. maybe i've been on some light speed travel lately.
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