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1+1+1+1...sum

psyduck
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3/24/2014 7:29:23 AM
Posted: 2 years ago
Let's say Series A is 1+2+3+4..., which equals -1/12.
If we add zero to it, it shouldn't change it's value.
So a series B equal to 0+1+2+3+4... should equal -1/12 as well.
And if that's the case, then you can subtract series B from series A and get 1+1+1+1+1...=0.
Yet it is supposed to be -1/2. Why is that?
Bannanawamajama
Posts: 125
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3/24/2014 8:56:28 AM
Posted: 2 years ago
Honestly I'm not entirely sure what you are saying here.

First your series A should go to infinity, not -1/12 unless Im misinterpreting it.

Series B should indeed go to the same value as series A, although thats still infinity.

Again, not sure why A-B should be equal to -1/2? As you said, the two series are equal, so subtracting them should equal 0, which it does.
Sswdwm
Posts: 1,398
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3/24/2014 9:22:54 AM
Posted: 2 years ago
At 3/24/2014 7:29:23 AM, psyduck wrote:
Let's say Series A is 1+2+3+4..., which equals -1/12.
If we add zero to it, it shouldn't change it's value.
So a series B equal to 0+1+2+3+4... should equal -1/12 as well.
And if that's the case, then you can subtract series B from series A and get 1+1+1+1+1...=0.
Yet it is supposed to be -1/2. Why is that?

1+2+3+4... Is a different infinite sum to 1+1+1+1....

I don't pretend to be an expert in divergent infinite series, but I do remember there is a distinction between a limit and a sum. Convergent series's sum equals their limit, but not for divergent ones.

http://en.m.wikipedia.org...;

Meh..
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Subutai
Posts: 3,165
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3/24/2014 12:56:24 PM
Posted: 2 years ago
At 3/24/2014 7:29:23 AM, psyduck wrote:
Let's say Series A is 1+2+3+4..., which equals -1/12.
If we add zero to it, it shouldn't change it's value.
So a series B equal to 0+1+2+3+4... should equal -1/12 as well.
And if that's the case, then you can subtract series B from series A and get 1+1+1+1+1...=0.
Yet it is supposed to be -1/2. Why is that?

This makes no sense for two reasons.

One, the series starting at n+1 of the series from n to i (where i is the nth term minus one) plus n itself it always going to be above 1/12 (1+2=3, so 1+2+3... has to be greater than 1/12), and is certainly not negative, because the series starts at a positive number, and extends to infinity.

Second, 1+1+1+1... does not equal -1/2. Again, the numbers and all positive, and the answer with successive values of i is always greater, so it can't equal -1/2.

So this makes your conclusion wrong. 1+1+1+1... does not equal zero, either.
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Iredia
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3/24/2014 2:09:46 PM
Posted: 2 years ago
My view of infinite series is that it is an assumption required to make maths feasible. But in a logical sense, I think it fails. I don't understand how an infinite sum can be added, when the whole concept of an infinite sum suggests that there is no limit to what you can add; and hence no result can be obtained.
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Subutai
Posts: 3,165
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3/24/2014 2:53:10 PM
Posted: 2 years ago
At 3/24/2014 2:09:46 PM, Iredia wrote:
My view of infinite series is that it is an assumption required to make maths feasible. But in a logical sense, I think it fails. I don't understand how an infinite sum can be added, when the whole concept of an infinite sum suggests that there is no limit to what you can add; and hence no result can be obtained.

There are two kinds of infinite series - divergent, which do not add up to any finite number, and convergent, which do add up to a finite number. For example, adding the reciprocals of fibonacci numbers adds up to the reciprocal Fibonacci constant. This is proved by the ratio test. There are a number of other examples, too.
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Iredia
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3/24/2014 3:07:30 PM
Posted: 2 years ago
At 3/24/2014 2:53:10 PM, Subutai wrote:
At 3/24/2014 2:09:46 PM, Iredia wrote:
My view of infinite series is that it is an assumption required to make maths feasible. But in a logical sense, I think it fails. I don't understand how an infinite sum can be added, when the whole concept of an infinite sum suggests that there is no limit to what you can add; and hence no result can be obtained.

There are two kinds of infinite series - divergent, which do not add up to any finite number, and convergent, which do add up to a finite number. For example, adding the reciprocals of fibonacci numbers adds up to the reciprocal Fibonacci constant. This is proved by the ratio test. There are a number of other examples, too.

Noted. As an aside, what do you think of infinite lines being a paradox. The way I see it lines have a start point and end point. But an infinity lacks a limit and hence can't start or end, the same for an 'infinite line' (it can't start or end). How then can it be a line ?
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psyduck
Posts: 16
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3/24/2014 4:13:40 PM
Posted: 2 years ago
At 3/24/2014 3:07:30 PM, Iredia wrote:

Noted. As an aside, what do you think of infinite lines being a paradox. The way I see it lines have a start point and end point. But an infinity lacks a limit and hence can't start or end, the same for an 'infinite line' (it can't start or end). How then can it be a line ?

Lines are infinite by definition.

I found a somewhat satisfactory answer to my problem on another site. Also, a lot of people were under the misunderstanding that the sum is infinity. The limit certainly is infinite, but the actual values of the sums are finite.
Sswdwm
Posts: 1,398
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3/24/2014 4:25:46 PM
Posted: 2 years ago
At 3/24/2014 4:13:40 PM, psyduck wrote:
At 3/24/2014 3:07:30 PM, Iredia wrote:

Noted. As an aside, what do you think of infinite lines being a paradox. The way I see it lines have a start point and end point. But an infinity lacks a limit and hence can't start or end, the same for an 'infinite line' (it can't start or end). How then can it be a line ?

Lines are infinite by definition.

I found a somewhat satisfactory answer to my problem on another site. Also, a lot of people were under the misunderstanding that the sum is infinity. The limit certainly is infinite, but the actual values of the sums are finite.

That's what I said!

At least I got something right.....
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Iredia
Posts: 1,608
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3/24/2014 4:44:18 PM
Posted: 2 years ago
At 3/24/2014 4:13:40 PM, psyduck wrote:
At 3/24/2014 3:07:30 PM, Iredia wrote:

Noted. As an aside, what do you think of infinite lines being a paradox. The way I see it lines have a start point and end point. But an infinity lacks a limit and hence can't start or end, the same for an 'infinite line' (it can't start or end). How then can it be a line ?

Lines are infinite by definition.

I found a somewhat satisfactory answer to my problem on another site. Also, a lot of people were under the misunderstanding that the sum is infinity. The limit certainly is infinite, but the actual values of the sums are finite.

Please post the link to the site. And if lines are infinite, by definition, it follows that they infinitely recede and infinitely progress since lines are infinitely extended in both directions. As for the misunderstanding, I can understand that, the term infinite series suggests that infinity is the end result. Note: I didn't say it is, but that it suggests it.
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Subutai
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3/24/2014 9:30:03 PM
Posted: 2 years ago
At 3/24/2014 3:07:30 PM, Iredia wrote:
At 3/24/2014 2:53:10 PM, Subutai wrote:
At 3/24/2014 2:09:46 PM, Iredia wrote:
My view of infinite series is that it is an assumption required to make maths feasible. But in a logical sense, I think it fails. I don't understand how an infinite sum can be added, when the whole concept of an infinite sum suggests that there is no limit to what you can add; and hence no result can be obtained.

There are two kinds of infinite series - divergent, which do not add up to any finite number, and convergent, which do add up to a finite number. For example, adding the reciprocals of fibonacci numbers adds up to the reciprocal Fibonacci constant. This is proved by the ratio test. There are a number of other examples, too.

Noted. As an aside, what do you think of infinite lines being a paradox. The way I see it lines have a start point and end point. But an infinity lacks a limit and hence can't start or end, the same for an 'infinite line' (it can't start or end). How then can it be a line ?

Lines are, by the geometrical definition, infinite. Any finite "line" is a line segment, and is only an infinitesimal portion of a whole line. It is useful to think of lines outside of the real world, and to think of an infinite Cartesian plane to better understand the concept. No, an infinite line in the real world is impossible, but by its geometric definition, it is infinite.
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Floid
Posts: 751
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3/25/2014 10:46:17 AM
Posted: 2 years ago
At 3/24/2014 4:44:18 PM, Iredia wrote:
Please post the link to the site. And if lines are infinite, by definition, it follows that they infinitely recede and infinitely progress since lines are infinitely extended in both directions. As for the misunderstanding, I can understand that, the term infinite series suggests that infinity is the end result. Note: I didn't say it is, but that it suggests it.

Personal ignorance makes for poor argument. In the future it would probably be best to at least look up the definition of very well defined terms before you make silly assumptions about what they mean.
Iredia
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3/25/2014 11:26:24 AM
Posted: 2 years ago
At 3/25/2014 10:46:17 AM, Floid wrote:
At 3/24/2014 4:44:18 PM, Iredia wrote:
Please post the link to the site. And if lines are infinite, by definition, it follows that they infinitely recede and infinitely progress since lines are infinitely extended in both directions. As for the misunderstanding, I can understand that, the term infinite series suggests that infinity is the end result. Note: I didn't say it is, but that it suggests it.

Personal ignorance makes for poor argument. In the future it would probably be best to at least look up the definition of very well defined terms before you make silly assumptions about what they mean.

Noted.
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AnDoctuir
Posts: 11,060
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3/26/2014 9:29:20 AM
Posted: 2 years ago
At 3/26/2014 9:21:44 AM, TheGreatAndPowerful wrote:
At 3/25/2014 12:01:25 PM, AnDoctuir wrote:
http://www.debate.org...

This is the first useful thing you've ever posted.

My a-ss.
WheezySquash8
Posts: 130
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4/17/2014 4:15:40 PM
Posted: 2 years ago
At 3/24/2014 7:29:23 AM, psyduck wrote:
Let's say Series A is 1+2+3+4..., which equals -1/12.
If we add zero to it, it shouldn't change it's value.
So a series B equal to 0+1+2+3+4... should equal -1/12 as well.
And if that's the case, then you can subtract series B from series A and get 1+1+1+1+1...=0.
Yet it is supposed to be -1/2. Why is that?

I'm confused on what you're saying, but that may be because I'm an idiotic teenager.
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tahir.imanov
Posts: 272
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4/17/2014 7:30:39 PM
Posted: 2 years ago
At 3/24/2014 7:29:23 AM, psyduck wrote:
Let's say Series A is 1+2+3+4..., which equals -1/12.
If we add zero to it, it shouldn't change it's value.
So a series B equal to 0+1+2+3+4... should equal -1/12 as well.
And if that's the case, then you can subtract series B from series A and get 1+1+1+1+1...=0.
Yet it is supposed to be -1/2. Why is that?

Actually you get it wrong. search for Rienman-Zeta functions
Z(n) = 1/1^n + 1/2^n + 1/3^n + ....................
Normally this function works for Natural numbers n.
For n = 1, sum is infinite.
For n=2, sum is (pi^2)/6, and etc.
What Rienman does, he extends n for negative numbers and for complex numbers.
Z(-n) = -(B_{n+1})/(n+1)
So, n=-1, sum is -1/12.
And Z(-1) = 1+2+3+.......
So 1+2+3+.............=-1/12.
For all, negative even integers Zeta is 0.
According Rienman, for Re(n) between 0 and 1 all zeros on line Re(0.5).
This is red.
Ore_Ele
Posts: 25,980
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4/18/2014 1:14:56 PM
Posted: 2 years ago
At 3/24/2014 7:29:23 AM, psyduck wrote:
Let's say Series A is 1+2+3+4..., which equals -1/12.
If we add zero to it, it shouldn't change it's value.
So a series B equal to 0+1+2+3+4... should equal -1/12 as well.
And if that's the case, then you can subtract series B from series A and get 1+1+1+1+1...=0.
Yet it is supposed to be -1/2. Why is that?

It needs to be noted that 1+2+3+4+... does not "equal" -1/12, but that it's summation (after some serious mental stretches) is equal to -1/12. Of course, "summation" when used in these forms makes all numbers meaningless.

After all, the "proof" relies on number shifting with infinite numbers. Which should automatically be shot down by any rational person.

Lets do our own example to show that number shifting is not a logical step to make a proof. Let's assume S = 1+2+3+4+.... = -1/12

As pointed out, S + 0 = 0+1+2+3+...

so S - (S + 0) = (1-0) + (2-1) + (3-2) + (4-3) + ....

This can be simplified to S - S + 0 = 1+1+1+1+...

Or 0 = 1+1+1+1+1+...

You can also mash this up further by just shifting the terms further, using S+0+0+0, which will get you 0 = 1+2+3+3+3+3+...
That can turn -3+0=3+3+3+3+...

Or -3=3+3+3+3+...

divide by 3 and you find...

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

So we find that -1 = 0
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AlbinoBunny
Posts: 3,781
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4/19/2014 5:16:37 AM
Posted: 2 years ago
At 3/24/2014 7:29:23 AM, psyduck wrote:
Let's say Series A is 1+2+3+4..., which equals -1/12.
If we add zero to it, it shouldn't change it's value.
So a series B equal to 0+1+2+3+4... should equal -1/12 as well.
And if that's the case, then you can subtract series B from series A and get 1+1+1+1+1...=0.
Yet it is supposed to be -1/2. Why is that?

Supposedly, it's a useful value (the golden nugget) we can take away from the summation, but not the actual value of the summation. Also apparently it has actual utility, but I can't personally confirm that. Or something like that...

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