A false midnight

Posted Mar 22, 2014 0:03 UTC (Sat) by mathstuf (subscriber, #69389)
In reply to: A false midnight by nybble41
Parent article: A false midnight

> Usually one doesn't consider the set an object was *selected from* to be an identifying characteristic of the object.

Well, in algebra "1 - 1 + 1 - 1 + …" is undefined since algebra cannot reach the end; in the realm of infinite series, ½ is a valid value for the series (and the only one). There's a similar thing with any of ζ(n) when n is a negative odd integers (ζ(-1) = 1 + 2 + 3 + 4 + … = -1/12, ζ(-3) = 1 + 8 + 27 + 64 + … = 1/120, etc.). Computations definitely rely on the context in which they reside; I see no reason why numeric values would be exempt.

A false midnight

Posted Mar 22, 2014 9:54 UTC (Sat) by Jandar (subscriber, #85683) [Link] (2 responses)

ζ(n) with negative odd n is infinite.

A false midnight

Posted Mar 22, 2014 10:46 UTC (Sat) by mathstuf (subscriber, #69389) [Link] (1 responses)

Depends on the context[1] :) . Each series resulting from the ζ(n) with n as a negative, odd integer has a single, useful value which can be used in its place when it occurs in equations (physics, chemistry, etc.).

[1]https://en.wikipedia.org/wiki/Particular_values_of_Rieman...

A false midnight

Posted Mar 22, 2014 15:23 UTC (Sat) by Jandar (subscriber, #85683) [Link]

It's embarrassing to see how much one can forget. My mathematical studies lie some 20 years in the past and almost anything about sheaf and germs is lost.