John Cowan wrote:
> So you argue that the sequence (2) is both increasing (there are no
> nonincreasing pairs) and nondecreasing (there are no increasing pairs)?
>   

Yes.   When you define it that way, there are bunch of basic proofs that 
come out
simpler.

Why do you need the extra baggage of "sequences of length greater than 
or equal
to two?"    Why not "three" or "917"?     It's easier if you say 
whatever you can
with respect to finite sequences in general.



> Then you are in the position of claiming that a sequence can be increasing
> even though it contains no increasing pairs, and likewise for the other
> predicates.  I find it farfetched to call that natural.
>
> But then I find axiomatic logic (as opposed to natural deduction)
> pretty retchworthy.
>   

That's ironic.

-t



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