Re: Date for Last Common Ancestor?
CHESSONP (chessonp@aol.com)
16 Aug 1996 11:13:03 0400
In article <3213B039.4A28@megafauna.com>, Stephen Barnard
<steve@megafauna.com> writes:
>
>CHESSONP wrote:
>>
>>
>> An example. Let I_k be the interval of real numbers greater than 1/k
and
>> less than 1+1/k, or in more familiar notation, (1/k, 1+1/k). This
>> interval has length 1+2/k. If we consider the sequence of interval
lengths
>> {1+2/k} obtained from the associated sequence of intervals {I_k}, we
see
>> that the lengths are strictly decreasing. However, the sequence of
lengths
>> does not go to zero, but rather to a nonzero number, namely one.
>
>I don't see how this applies to my argument. Your example operates in an
>entirely different domain (infinite sets of real numbers in some bounded
>interval), while my argument deals with finite sets. Furthermore, your
>example doesn't make use of the critical inheritance property (everyone
has
>exactly one mother) which is the basis for my argument.
>
>You can't disprove an argument by presenting an entirely different
problem
>and saying that it doesn't lead to the same answer.
>
>Thanks for trying, though.
>
> Steve Barnard
>
>
The point of the example is to illustrate the fault in your logic. A
decreasing sequence of numbers may not converge to anything. A decreasing
sequence of numbers that is bounded will converge to its greatest lower
bound which need not be zero. A decreasing sequence of positive whole
numbers will converge to zero, but any finite segment of this sequence
will not. A nonincreasing sequence of positive whole numbers will
converge to its greatest lower bound, which may not be zero.
You cannot claim that the size of your set of great .... grand mothers
reaches one at some point simply because each set (going backward by
generation) is not larger than the previous one. On logical grounds alone
the number of females in this "lca founding population" could be any
number no larger than the smallest known human population size at some
time.
