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There is no n.sequence between 0 and ωThen infinity means only an interval on the real line that can be extended by a factor 2 when _all_ its numbers (including all n+n-sequences) are doubled. Hilbert, Cantor, and others call that potential infinite.
without a n+n.sequence between 0 and ω.
'Infinite' does not mean what you want it to mean.
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