Re: ** says: Definition: sum{i in N} i = 0

In article <4689c639@xxxxxxxxxxxxxxxxxxx> Tony Orlow <tony@xxxxxxxxxxxxx> writes:
*** T. Winter wrote:
....
No. The finite case is clear. For "the sum of all" you need definition,
although you do not think so. Within analysis the sum of all is undefined.
Within topology the sum can be defined if you compactify the reals, but
the result will depend upon the manner of compactification. Within set
theory the sum is in general undefined, but can be defined, as I already
wrote oh so many articles ago; but at that time you rejected my definition.
It is your assumption that a definition in one discipline should be
identical to a definition in another discipline leads you astray.

Hi *** - question -

Why would you define it that way? I mean, what is the motivation or
justification to say the sum is nought?

Why not? The only motivation and justification is that that definition
cannot be proven wrong using ordinary mathematics. But perhaps I should
have said that the sum was -1/12...
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

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