🚀 go-pugleaf

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

[I apologize to those readers of this newsgroup who took this obvious error
in their stride. However, I felt it was worth correcting in view of the
intended audience (those with no prior understanding of the concept of
cardinality).]
--
Sandy Nicholson (sandy@festival.ed.ac.uk)
Department of Mathematics and Statistics, Edinburgh University, Scotland