What is the sum of all real numbers?

Note by Adharsh M
2 years, 2 months ago

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is it 0?

Adharsh M - 2 years, 2 months ago

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No, it is not.

Calvin Lin Staff - 2 years, 2 months ago

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It's \infty.

Munem Shahriar - 2 years, 2 months ago

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Can you justify why?

Calvin Lin Staff - 2 years, 2 months ago

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@Calvin Lin Because there are infinitely many real numbers.

Munem Shahriar - 2 years, 2 months ago

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@Munem Shahriar And so?

Calvin Lin Staff - 2 years, 2 months 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 - 2 years, 1 month ago

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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?)

Calvin Lin Staff - 2 years, 1 month ago

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Mr.Calvin Lin, could you please explain, what actually you want to convey.

Adharsh M - 2 years, 1 month ago

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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 xx with x-x to make the sum of infinitely many xx=0 x -x = 0" not work?

Calvin Lin Staff - 2 years, 1 month ago

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why doesn't it work?

Adharsh M - 2 years, 1 month ago

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Read the wiki, esp the last section.

Calvin Lin Staff - 2 years, 1 month ago

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which wiki, which section, please explain

Adharsh M - 2 years, 1 month ago

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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.

Calvin Lin Staff - 2 years, 1 month ago

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