🚀 go-pugleaf

In article <26319@castle.ed.ac.uk>, sandy@festival.ed.ac.uk (Sandy Nicholson) writes:
>In article <1992Sep25.113936.19246@news.nd.edu>, nik@csgi48.dcs.leeds.ac.uk
>(Nik Silver) writes (much deleted):
>
>|> On the other hand, when we consider the (countably) infinite numbers w and
>|> w+1 we find that they are ordinally different (w+1 comes after w) but
>|> have the same cardinality. They have the same cardinality because we can
>|> define a bijection f from w+1 to w as follows:
>|> 	f(n)   = n+1 for n finite,
>|> 	f(w)   = w,
>|> 	f(w+1) = 0.
>
>I presume this was a momentary lapse---clearly the (von Neumann) ordinal w+1
>is not a member of the ordinal w+1, any more than w is a member of w.
>The bijection should be something along the lines of:
>
>      f(n) = n+1  for all finite n
>      f(w) = 0

Sandy Nicholson is quite correct, here, and I apologise for any confusion
I may have caused. (When I read the correction, I had to pause for quite
some time before seeing my mistake.) What has happened is that I had
confused the set X with the set of ordinals up to and including X (where X is
w or w+1).

Was it a momentary lapse, or really a lack of understanding on my part? I
thank you for the benefit of the doubt :-).

-- 
Nik ``nik@scs.leeds.ac.uk'' Silver