which wiki, which section, please explain
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Adharsh M
·
3 weeks, 5 days ago

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@Adharsh M
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The absolutely convergent wiki that I linked to. Read through the entire wiki, esp since it sounds like you are unfamiliar with this concept.
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Calvin Lin
Staff
·
3 weeks, 5 days ago

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why doesn't it work?
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Adharsh M
·
3 weeks, 5 days ago

Mr.Calvin Lin, could you please explain, what actually you want to convey.
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Adharsh M
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3 weeks, 5 days ago

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@Adharsh M
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The sum of all real numbers is undefined. This is because the summation is not absolutely convergent, and hence we cannot assign a value to it.

Why does the naive approach of "pairing up \(x\) with \(-x\) to make the sum of infinitely many \( x -x = 0\)" not work?
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Calvin Lin
Staff
·
3 weeks, 5 days ago

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if I say that all the real numbers will have their negative pair ,example 5 and -5,so similarly for infinity there will be -infinity which will sum to 0
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Adharsh M
·
3 weeks, 6 days ago

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@Adharsh M
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That's a good thought. Under what scenarios can we do? (Maybe the question to answer first is: what are we doing here?)
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Calvin Lin
Staff
·
3 weeks, 6 days ago

@Calvin Lin
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Since there are infinitely many real numbers or uncountably many real numbers so we can't determine there sum.
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Munem Sahariar
·
1 month ago

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@Munem Sahariar
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So, you are changing your answer from "\( \infty\)" to "undefined"?
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Calvin Lin
Staff
·
1 month ago

@Munem Sahariar
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It is very rare for an equation to have 2 answers.

At the very most, it would be "Under different interpretations". For example, \( 1 + 2 + 3 + \ldots \) would be infinity in the usual calculus treatment of infinite sums, but could be \( - \frac{1}{12} \) under the analytic continuation of \( \sum n^s \). As such, can you clarify under which interpretation we get the answer of "\(\infty\)", and under which interpretation we get the answer of "undefined"?
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Calvin Lin
Staff
·
3 weeks, 6 days ago

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TopNewestwhich wiki, which section, please explain – Adharsh M · 3 weeks, 5 days ago

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absolutely convergent wiki that I linked to. Read through the entire wiki, esp since it sounds like you are unfamiliar with this concept. – Calvin Lin Staff · 3 weeks, 5 days ago

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why doesn't it work? – Adharsh M · 3 weeks, 5 days ago

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– Calvin Lin Staff · 3 weeks, 5 days ago

Read the wiki, esp the last section.Log in to reply

Mr.Calvin Lin, could you please explain, what actually you want to convey. – Adharsh M · 3 weeks, 5 days ago

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absolutely convergent, and hence we cannot assign a value to it.

The sum of all real numbers is undefined. This is because the summation is notWhy does the naive approach of "pairing up \(x\) with \(-x\) to make the sum of infinitely many \( x -x = 0\)" not work? – Calvin Lin Staff · 3 weeks, 5 days ago

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if I say that all the real numbers will have their negative pair ,example 5 and -5,so similarly for infinity there will be -infinity which will sum to 0 – Adharsh M · 3 weeks, 6 days ago

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– Calvin Lin Staff · 3 weeks, 6 days ago

That's a good thought. Under what scenarios can we do? (Maybe the question to answer first is: what are we doing here?)Log in to reply

is it 0? – Adharsh M · 1 month ago

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– Munem Sahariar · 1 month ago

It's \(\infty\).Log in to reply

– Calvin Lin Staff · 1 month ago

Can you justify why?Log in to reply

– Munem Sahariar · 1 month ago

Because there are infinitely many real numbers.Log in to reply

– Calvin Lin Staff · 1 month ago

And so?Log in to reply

– Munem Sahariar · 1 month ago

Since there are infinitely many real numbers or uncountably many real numbers so we can't determine there sum.Log in to reply

– Calvin Lin Staff · 1 month ago

So, you are changing your answer from "\( \infty\)" to "undefined"?Log in to reply

– Munem Sahariar · 4 weeks, 1 day ago

No. \(\infty\) and undefined both are my answers.Log in to reply

At the very most, it would be "Under different interpretations". For example, \( 1 + 2 + 3 + \ldots \) would be infinity in the usual calculus treatment of infinite sums, but could be \( - \frac{1}{12} \) under the analytic continuation of \( \sum n^s \). As such, can you clarify under which interpretation we get the answer of "\(\infty\)", and under which interpretation we get the answer of "undefined"? – Calvin Lin Staff · 3 weeks, 6 days ago

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– Calvin Lin Staff · 1 month ago

No, it is not.Log in to reply