Re: Two results of set geometry

WM wrote:

The set of natural numbers is not a natural number. The set N has
omega elements but it has no numerical seize.

The set of natural numbers, if it could exist, would be equivalent to
another natural number. Therefore it cannot exist. (Tip, hint: there
is a bijection between sets and naturals).

Han de Bruijn

.

Relevant Pages

  • Re: Two results of set geometry
    ... Han de Bruijn writes: ... (Tip, hint: there ... is a bijection between sets and naturals). ... Where might one find this bijection described? ...
    (sci.math)
  • Re: Two results of set geometry
    ... omega elements but it has no numerical seize. ... is a bijection between sets and naturals). ... this bijection exists in Bruijnland and perhaps ...
    (sci.math)
  • Re: Two results of set geometry
    ... (Tip, hint: there ... is a bijection between sets and naturals). ... Where might one find this bijection described? ... But a stronger result is that ...
    (sci.math)
  • Re: infinity
    ... > Yes, for your proposed mapping between N and P, ... the largest element would not map to the ... so our bijection never runs into any such endpoint and ... what is the last element in the mapping of naturals to evens? ...
    (sci.math)
  • Re: infinity
    ... In the latter case, there is a bijection, ... >> regarding the evens, and ask how many bits each set's elements has, the evens ... like the bijection between the naturals and the ... > infinite sets, there is no way to use a "running out of" argument, ...
    (sci.math)
Loading