Axiom of Choice and Continuum Hypothesis
What are the real numbers? At least the question has become somewhat clearer since it was posed in Section 1: any satisfactory answer must provide a frame of reference for mathematical activity, in particular for proving theorems in analysis. There seem to be two aspects of this activity that go hand in hand: on the one hand there is what active mathematicians call “intuition” (without, if they are wise, going into its psychological details), or “thinking in concepts”, on the other the mathematical formalism which, with the help of symbolic logic, can be refined into a precision tool.
KeywordsFormal Framework Continuum Hypothesis Mathematical System Theory Uncountable Cardinal Precision Tool
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