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On 10.01.2025 21:06, joes wrote:Good. It is not true for the infinite sets.Am Fri, 10 Jan 2025 20:17:37 +0100 schrieb WM:Of course. Otherwise you would have to find a counterexample.On 10.01.2025 19:28, joes wrote:But it is true for every naturalAm Fri, 10 Jan 2025 18:21:43 +0100 schrieb WM:>No, I expect it is true for all natural numbers, none of which isI have no expectations about cardinality. I know that for everyYou wrongly expect this to hold in the infinite.
finite initial segment the even numbers are about half of the
natural numbers.
This does not change anywhere. It is true up to every natural
number.
infinite.
Mathematics is all about formalising.(if you formalise it correctly)!Irrelevant.
∀n ∈ ℕ: |{1, 2, 3, ..., 2n}|/|{2, 4, 6, ..., 2n}| = 2.Those are not N and E.
No. For n->oo, G is both the set {2, 4, ..., 2n} and {2, 4, ..., 42n};That doesn't make it true for N and G.I am not interested in these letters but only in all natural numbers.
All natural numbers are twice as many as all even natural numbers. If
your N and G denote all natural numbers and all even numbers, then 2 is
true also for them.
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