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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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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
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[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
is it 0?
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No, it is not.
It's ∞.
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Can you justify why?
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Because there are infinitely many real numbers.
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And so?
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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That's a good thought. Under what scenarios can we do? (Maybe the question to answer first is: what are we doing here?)
Mr.Calvin Lin, could you please explain, what actually you want to convey.
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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?
why doesn't it work?
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Read the wiki, esp the last section.
which wiki, which section, please explain
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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.