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Am 14.06.2024 um 20:52 schrieb Jim Burns:Btw. Did I mention my cat?On 6/14/2024 12:39 PM, WM wrote:Just seen here:
"number(s)" (WM) seems to refer to "natural number(s)" in this context.
Actually, we do not have to assume that, since it can be proved (in the context of mathematics/set theory).WM (Proof by contradiction):
[Assume:] Every number has ℵo successors.
An e IN: card({m e IN : m > n}) = ℵo.
Huh?! Just a silly (psychotic) claim. If _every_ number "is subtracted" (based on "the set of numbers+their successors"), then NO numbers (and hence no successors) "remain" [in the new/resulting set]. (After all, the successors of any number are numbers too.*)If every number is subtracted the successors remain.
What did WM prove here? That he's a complete idiot?
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*) An e IN: {m e IN : m > n} c IN.
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