Re: When a mathematician makes a mistake...


juanpool@xxxxxxxxx wrote:
Some one remember Srinivasa Ramanujan ? Well him in the view of
standars mathematician was prune to do a lot of mistakes, because for
example he used not converging series in some of his poofs, but ¿ this
is wrong ? Think about this 2 sequences of numbers :

s1(n) = sum_{1,2,...,n} 1/n

s2(n)= 2 * s1(n)

obiously:

lim_{n->infinity} s1(n) = infinity

lim_{n->infinity} s2(n) = infinity

but let be :

s3(n) = s1(n)/s2(n) = 1/2 for all n

then :

lim_{n->infinity} s3(n) = 1/2

So, although s1(n) and s2(n) diverges, they contains some
"mathemátical information" as sequences of numbers, so using them as
formal objets could lead to potential mathemátical results. [...]

One of the recent issues of the _American Mathematical Monthly_ has an
article about nonstandard analysis, where you _can_ treat
1 + 1/2 + 1/3 + ... as having an actual value.

--- Christopher Heckman

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