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On 11/24/2024 2:42 PM, WM wrote:Endsegmentes can change by 1 element. Therefore their number of elements can change by 1.On 24.11.2024 20:26, Jim Burns wrote:Finite cardinalities can change by 1.What we mean by>
|E(k)| ≤ |E(k+1)|
is that
there is a one.to.one function
from E(k) to E(k+1)
The successor operation, for example.
What I mean is the fact that
∀k ∈ ℕ: |E(k+1)| = |E(k)| - 1
whereas Cantor's ℵo is a very unsharp measure.
Infinite cardinalities are larger thanInfinite cardinalities are to coarse to indicate that change. But the change takes place:
each finite cardinality,
and cannot change by 1.
ℕ is the set of each and only finite cardinalities.ℕ cannot change by 1 Element.
|ℕ| isn't a finite cardinality.
|ℕ| cannot change by 1.
From two examples above you can see a change of an infinite set by 1 element. A proper measure will be able to indicate that.Cantor's nonsense has many faces.Cardinalities which cannot change by 1
It i not suitable for serious maths.
do not change by 1 when they're called unserious.
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