>week 1 of real analysis
>professor asks the whole class what the real numbers are
>half the class only comfortable with integers while the other half butchers the definition of rationals and refers to them as 'fractions'
>ask the prof if we can actually go through and CONSTRUCT them from first principles in depth
>"we shall take the real numbers as an axiom and let them be given" and defines them via dedekucks cuts
>ask if we can go more in depth on the construction from starting principles
>"The complete ordered fields constructed by the Dedekind and Cauchy methods are isomorphic and thus theorems of ZF. R will be given to us in this course"
Is this a joke ? isnt the point of real analysis to build up and understand real numbers in a formal and rigorous way?
>professor asks the whole class what the real numbers are
>half the class only comfortable with integers while the other half butchers the definition of rationals and refers to them as 'fractions'
>ask the prof if we can actually go through and CONSTRUCT them from first principles in depth
>"we shall take the real numbers as an axiom and let them be given" and defines them via dedekucks cuts
>ask if we can go more in depth on the construction from starting principles
>"The complete ordered fields constructed by the Dedekind and Cauchy methods are isomorphic and thus theorems of ZF. R will be given to us in this course"
Is this a joke ? isnt the point of real analysis to build up and understand real numbers in a formal and rigorous way?
