Unformatted text preview: Infnite Ordinals and Cardinals • ²or ±nite ordinals and cardinals, the distinction is linguistic and conceptual, not mathematical. • Trans±nite ordinal numbers were introduced by Cantor in 1883. Order types of wellordered sets. Noncommutative arithmetic. (More to come on the reason for their discovery.) • Trans±nite cardinal numbers were introduced by Cantor in 1895. Some algebraic rules. Hyperreal Numbers • More or less invented by Abraham Robinson in 1960s to allow working with diFerentials in a rigorous matter. “Nonstandard analysis.” Not widely used. (Maybe more to come.)...
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 Fall '10
 wen
 Logic, Real Numbers, Georg Cantor, Cantor, Real analysis studies

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