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Am Sat, 12 Oct 2024 19:49:23 +0200 schrieb WM:Cardinality is nonsense. Density is numbers per places for every finite set.On 10.10.2024 21:54, joes wrote:Taking "density" here to mean cardinalityAm Thu, 10 Oct 2024 20:53:07 +0200 schrieb WM:But the doubles are larger. Hence after doubling the set has a smallerOn 10.10.2024 20:45, Alan Mackenzie wrote:Exactly! There are furthermore no infinite doubles of naturals (2n).WM <wolfgang.mueckenheim@tha.de> wrote:>There are no infinite n = natural numbers.If all natnumbers are there and if 2n is greater than n, then theFor any finite n greater than zero, 2n is greater than n. The same
doubled numbers do not fit into ℕ.
does not hold for infinite n.
density and therefore a larger extension on the real line. Hence not all
natural numbers have been doubled.
The real line reaches until, but does notThen double ℕ U {ω}.
include omega, no matter your step size.
What value do you suppose n^2More difficult to determine than 2n.
and n^n diverge to?
Then you are outside of basic mathematics. The double number is larger than the doubled - in every case, even for infinite numbers.No! Actual infinity already includes all doubles of all numbers.Then there is no complete set. The doubling can be repeated andAdditionally: if n is finite, so is 2n. It cannot go beyond w.Deplorable. But note that all natural numbers are finite and followNo. Not even close.Either doubling creates new natural numbers. Then not all have beenNumbers multiplied by 2 do not remain unchanged.
doubled. Or all have been doubled, then some products fall outside
of ℕ.
this law: When doubled then 2n > n. If a set of natural numbers is
doubled, then the results cover a larger set than before..
repeated. Always new numbers are created. Potential infinity.
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