Mike Deeth wrote in message <3681B99D.66997C67@ashland.baysat.net>... > > >The table below shows a bijection between a Natural number and a Set with the >same >number of members. None can doubt this bijection continues into the infinite. >Lets say that the last row of the table contains the infinite set of all natural > >numbers. What natural number is it in bijection with? (Remember, the number >must >be a Natural) > > N Set-of-N >--------------------- > 1 {1} > 2 {1,2} > 3 {1,2,3} > 4 {1,2,3,4} > 5 {1,2,3,4,5} > . . > . . > . . > ? {1,2,3, ... } > >
That's a bijection between the set of *finite* sets of the form {1, 2, 3, ..., n} and the set of natural numbers. Whilst it 'continues into the infinite', at no point does it map an infinite set to an infinite natural. All the Set-of-N things in your table are finite sets. All Natural numbers are finite.
