Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/15/2024 1:53 PM, WM wrote:

On 15.11.2024 18:54, Jim Burns wrote:
 > On 11/15/2024 5:04 AM, WM wrote:
  >> For infinite figures
 >> we use the analytical limit
 >> as is normal in mathematics.
 >
 > The reason you (WM) give is that
 > ☠⎛ whatever is true of all finite
 > ☠⎝ is also true of the infinite.
 Not "whatever" but well-established rules.
 >
 > You (WM) are misinterpreting the infinite as
 > ☠( just like the finite, but bigger.
 You are believing that the infinite can do magic. I believe that limits of simple sequences can be calculated. The sequence 1/5, 1/5, 1/5, ... has the limit 1/5 after all terms. It does never deviate.
 >
 > The finite are the countable.to from.nothing.
 > Anything countable.to from.nothing is finite.
 > It's what.we.mean.
 Either we can calculate the infinite by means of the finite relations, or this will forever remain impossible. Only in the latter case your argument is acceptable. But why do you believe in Cantor's bijections if the infinite can disobey all logic?
 If it is possible that the set {10^10^10^n, 10^10^10^m, n, m ∈ ℕ} has precisely as many elements as the set of algebraic numbers (i.e., if there can exist a bijection), then there is no trust in bijections.
 If the intervals [n - 1/10, n + 1/10] can infinitely often cover the real line, then there is no trust in geometry.
  > And our sets do not change.
 Then the density 1/5 will never change. Then never a new guest can be accomodated in the fully occupied Hilbert's hotel.

Ugg, an infinite set is never exhausted. Taking a gallon of water out of an infinite pool of water means you are holding a gallon water, but the infinite pool is still infinite. The same. Taking an infinite amount of water means the pool is still full of water.