What is your favorite way of explaining
>what the real numbers are
>what arithmetic operations (+,-,*,/) on real numbers are
>what infinite decimal notation means
>how real numbers relate to real-world lengths, times, volumes, and masses
Do you prefer axioms or explicit models? If axioms, what version of the completeness axiom do you like, and do you prefer to make Archimedes' Property a separate axiom or a consequence of completeness? If models, which model is the most intuitive? Do you prefer constructive reals or classical reals, and if constructive, which kind? Which operations do you prefer to define in terms of other operations, and which do you prefer to simply list axioms for? Do you think epsilon-N limits are the best way to define infinite decimals, or do you think another definition like the ones based on supremums or nested intervals is better? How would you explain to someone why 0.999... = 1? Should 0^0 be defined as 1? Do you think real numbers are schizophrenic infinitist nonsense, not even redeemable by Bishop's work on constructive analysis? How do you justify applying theorems about the mathematical abstraction that is real numbers to real world quantities?
>what the real numbers are
>what arithmetic operations (+,-,*,/) on real numbers are
>what infinite decimal notation means
>how real numbers relate to real-world lengths, times, volumes, and masses
Do you prefer axioms or explicit models? If axioms, what version of the completeness axiom do you like, and do you prefer to make Archimedes' Property a separate axiom or a consequence of completeness? If models, which model is the most intuitive? Do you prefer constructive reals or classical reals, and if constructive, which kind? Which operations do you prefer to define in terms of other operations, and which do you prefer to simply list axioms for? Do you think epsilon-N limits are the best way to define infinite decimals, or do you think another definition like the ones based on supremums or nested intervals is better? How would you explain to someone why 0.999... = 1? Should 0^0 be defined as 1? Do you think real numbers are schizophrenic infinitist nonsense, not even redeemable by Bishop's work on constructive analysis? How do you justify applying theorems about the mathematical abstraction that is real numbers to real world quantities?
