Re: subseries, correction to previous

I just realized that I when I pontificated about the way to define
subsequence, I had forgotten that the point was to get to subseries. I
retract my criticism of your book. For the purpose of defining
subseries one does want the 1 to 1 condition for f (order is not
needed). For issues involving simple convergence of sequences,
however, the cofinal condition is all one needs.

Mike


The reason I ask, is the following definition of subseries in my calc
book:

Let f be a function whose domain is N and whose range is an infinite
subset of N, and assume that f is 1-to-1 on N. Let Sigma(a(n)) and
Sigma (b(n)) be two series s.t.

b(n)=a(f(n)) if n is in N

Then Sigma(b(n)) is said to be a subseries of Sigma(a(n))

As far as I can tell, this definition doesn't imply anything about the
order?

thanks
mr

.

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