A Formal Background to Mathematics: Logic, sets, and numbers. 2 v |
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Appendix arbitrary letter arbitrary strings Axiom of Choice Bourbaki cetera Chapter Coll collectivising concept conventional defined denote arbitrary sets denote distinct letters denote the theory denotes a letter discussion element equal equivalence relation equivalent example explicit axiom expressed false finite formal definition formal language formal sentence formal theory formalisation function f function with domain Hence informal mathematics injective function instance intended intuitive Kleene letter not appearing logical metalanguage metamathematical metatheorems natural number notation obtained by adjoining ordered pair phrase precisely Problem proof methods provable prove quotient set Ran f reader real numbers reference relation remarks replacement rules routine proof semi formal proof sentence schema sequence set denoted set theory string denoted subset symbols theorem schema theory obtained true truth tables usually variable verified wherein ΤΘ