Wednesday, 24 April 2019

sequences and series - why does math "break" when it comes to certain topics?

For example,



1+2+3+...=1/12



or 2+4+8+...=1




What caused it to break? Are there some properties of real numbers that do this? Sorry if it's too vague because I was looking at group theory and there were things that didn't hold.



Another thing is why do some problems become ill-posed? For example, Wilkinson Polynomial, why do roots break by having too many multiplication of binomials?

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