Perplexed in Peoria  wrote or quoted:

> Regarding infinities without the use of limits:
> 
> Tim, I think you are wrong here.  Yes, working with the infinite
> in mathematics is subtle, and it takes some extra care.  The use
> of limits is the first method that mathematicians found to handle
> infinite sets rigorously.  It was an invention of the nineteenth
> century.  It is one way of achieving rigor, but it is not the
> only way.
> 
> During the twentieth century, several other methodologies have
> been discovered permitting rigor.  One of them is non-standard
> analysis, though that does not seem relevant here.  Another
> is "measure theory" - which is quite relevant.  Look into it.

Basically it seems to use integration - i.e. the limit of dx -> 0.

> You are just simply wrong to assert that talking about the
> infinite without using limits is a sign of mathematical
> ignorance.

I have looked back through what I wrote.  I can see no sign of
me saying that.  It seems to me that you would need to quote me
saying something along these lines to back up your claim.

You cannot simply talk about ratios between two inifite quantities.
so - unqualified mention of allele frequency in an infinite population 
makes no sense.

You *can* make coherent statements about the topic - either by
specifying a limit, by specifying a sampling stratgey (also a
form of limit) - or in a number of broadly-equivalent ways -
but unqualified discussion of frequencies in infinite populations
is still bad form.
-- 
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