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On 18.11.2024 22:58, FromTheRafters wrote:|N\{0}| = |N| = Aleph_0on 11/18/2024, WM supposed :On 18.11.2024 18:15, FromTheRafters wrote:WM brought next idea :>|ℕ| - |ℕ| = 0 because if you subtract one element from ℕ then you
have no longer ℕ and therefore no longer |ℕ| describing it.
You can still say it is a subset, like Cantor did with "reality".It has one element less, hence the "size" ℵo is a very unsharp measure.If you remove one element from ℕ, then you have still ℵo but no longerBut you do have now a proper subset of the naturals the same size as
all elements of ℕ.
before.
And |N\{2}| = Aleph_0.Subtracting an element is defined. |ℕ| - 1 is defined as the number ofIf |ℕ| describes the number of elements, then it has changed to |ℕ| -Minus one is not defined.
1.
elements minus 1.
There are infinitely many of them.The set of prime numbers is smaller.If you don't like |ℕ| then call this number the number of naturalWhy would I do that when it is the *SIZE* of the smallest infinite set.
numbers.
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