RATIONAL NUMBERS
Resources & Insights
Dirichlet’s Function and the Indicator of Rationals in the Architecture of Real Analysis
Dirichlet’s function marks rationals with 1 and irrationals with 0, creating a classic example from real analysis. Its behavior illustrates density, nowhere continuity, and the contrast between Riemann and Lebesgue integration. READ MORE...
Simplify ## \frac{x^2 - 9}{x^2 + 5x + 6} ##
Learn how to simplify ##\frac{x^2 – 9}{x^2 + 5x + 6}## using difference of squares and trinomial factoring while identifying excluded values and discontinuities. READ MORE...
Constructing Continuous Functions: Examples and Proofs
Learn how to build functions continuous at specific points, like integers or irrationals. Explore examples and proofs for constructing continuous functions. READ MORE...