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BRANCH OVERVIEW
Real analysis
Completeness, convergence, and rigorous approximation.
← All branches · Each sheet includes definitions, theorems, applications, and exercises with hints and worked solutions.
Real analysis
Completeness, convergence, and rigorous approximation.
- Completeness & sequencesCompleteness guarantees that approximations whose internal error vanishes have a limit in the space.
- Metric compactness & fixed pointsCompactness controls arbitrary covers; contraction controls successive approximations.
- Series & uniform convergenceA pointwise limit answers one input at a time; a uniform limit controls all inputs at once.