A topic within Analysis, itself one of 12 topics in that field and part of Mathematics.
2 works
William F. Trench
Builds single-variable and then multivariable real analysis from an explicit axiomatic account of the real numbers, treating completeness as the property that makes calculus rigorous rather than assumed.
link checked 17 Sept 2026Brian S. Thomson, Judith B. Bruckner & Andrew M. Bruckner
Covers the standard first course in real analysis but insists on constructing the real numbers and proving convergence results from first principles before any calculus is assumed.
link checked 17 Sept 2026