If you did then it did not work because it only works for non-zero positive even integers because the Bernoulli of 0 can either be -1/2 or 1/2]]>

That is a celebrated result and nowhere did I read it is an indeterminate series, but that it just converges to Euler's result.]]>

That is something I can not answer. I only have the tiniest bit of understanding of that page. Not enough to even comment.

]]>Thanks for clearing up the definition does not hold for Re(s) < 1. In other forums people were just stating it is an unexpected result and we have to live with it and I was thinking WHAT??!, the equality is altogether wrong, meaning the sum over ones.

My question is how analytic continuation does not address a new function all together? Is it because the transformation is unique; that is the key?

Cheers!

]]>Welcome to the forum!

The zeta function is defined like this

only when the sum converges which it clearly does not for s=0. So the above definition does not hold. Look here for how an analytic continuation is used:

]]>I want to comprehend what this means but it seems to me this just supersedes quantitative math.

Is there supposed to be a qualitative limited meaning to it?

Because if you forget the outcome is from zeta and just write 1 + 1 + 1 + ... = -1/2 this clearly is nonsense alone like that, as Hardy and Littlewood thought initially of it mailed by Ramanujan.

Math gurus enlighten me.

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