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No so for infinite. If you add 1 to ω you haven't changed the cardinality at all. But if you append a new number after ω then that new number is in a position w
by michaelochurch 16y ago
No so for infinite. If you add 1 to ω you haven't changed the cardinality at all. But if you append a new number after ω then that new number is in a position which doesn't exist anywhere in ω, and therefore it must be a larger ordinal.
It's worth noting that ordinal addition and multiplication are not commutative. 1+ω = ω ≠ ω+1