Re: 1-1/2+1/3-1/4+1/5-1/6+1/7

Jesse F. Hughes wrote:

S[x] = { S(z) | z in x }
= { y | (E z in x)(E n in N)(A m in N)(m > n -> y in S_m(z)) }

I do not see why that should be the same set as

T(x) = { y | (E n in N)(A m in N)(m > n -> (E z in x)(y in S_m(z))) }

So, you have to show that

(E z in x)(E n in N)(A m in N)(m > n -> y in S_m(z))

iff

(E n in N)(A m in N)(m > n -> (E z in x)(y in S_m(z)))

I don't believe it's so.

In the lucid notation by G. Frege:

lim S_n[N] = {N} . Hence S[N] = {N} . But also:
n -> oo

lim S_n[N] = lim N \ {0,1,2,3 .. ,n} = N \ lim {0,1,2,3 .. ,n} = N \ N
n -> oo n -> oo n -> oo

Hence: S[N] = {} . No ?

Is there a problem while interchanging a set difference with our limit ?

Han de Bruijn

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