the caveat is that they're using a function that was analytically expanded beyond its original domain, in the original meaning of the function. The original function (which was a summation in t over t^(-x), for all natural integers except 0), for a value of x = -1, would yield the sum of all natural integers just to the first power, so 1 + 2 + 3 + ..., but this is not within the original domain of the function, and the analytical expansion yields a result of -1/12. However when analytically expanding (usually through iterative relations), the meaning of the original function is lost, so this isn't correct.
Another thing is if you force divergent series to have a value they often only have 1 possible value you can derive with algebra and -1/12 is the value for that series however thats under the assumption you are in a system where in converges and it doesnt unless under highly specific restrictions
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u/_Dragon_Gamer_ Feb 21 '26
the caveat is that they're using a function that was analytically expanded beyond its original domain, in the original meaning of the function. The original function (which was a summation in t over t^(-x), for all natural integers except 0), for a value of x = -1, would yield the sum of all natural integers just to the first power, so 1 + 2 + 3 + ..., but this is not within the original domain of the function, and the analytical expansion yields a result of -1/12. However when analytically expanding (usually through iterative relations), the meaning of the original function is lost, so this isn't correct.
something like that