Mathematical Analysis generally, including Real Analysis, Harmonic Analysis, Complex Variable Theory, the Calculus of Variations, Measure Theory, and Non-Standard Analysis.
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Proving a function is continuous on all irrational numbers
Let $\langle r_n\rangle$ be an enumeration of the set $\mathbb Q$ of rational numbers such that $r_n \neq r_m\,$ if $\,n\neq m.$ $$\text{Define}\; f: \mathbb R \to \mathbb ...
