analysis--oxford-M2-real-analysis-I--theorems.dot

digraph {
    "Addition on R" -> "Triangle Law";
    "Addition on R" -> "Reverse Triangle Law";

    "Completeness of R" -> "Approximation Property";

    "Approximation Property" -> "Existence of Square Roots";

    "Completeness of R" -> "Archimedean Property of N";
    "Approximation Property" -> "Archimedean Property of N";

    "Completeness of R" -> "Well-ordered Property of N";
    "Approximation Property" -> "Well-ordered Property of N";

    // "Definition of Limit" -> "Tails Lemma";

    // "Definition of Limit" -> "Sandwiching Lemma";

    // "Definition of Limit" -> "Uniqueness of Limits";
    "Triangle Law" -> "Uniqueness of Limits";

    // "Definition of Limit" -> "Convergent sequence is bounded";
    "Triangle Law" -> "Convergent sequence is bounded";

    "Reverse Triangle Law" -> "Convergence => Convergence in absolute value"
    "Sandwiching Lemma" -> "Convergence => Convergence in absolute value"

    // "Definition of Limit" -> "All subsequences of convergent sequence are convergent";

    // "Definition of Limit" -> "Subsequences w/ different limits => Divergent sequence";

    "Definition of Limit" -> "Algebra of Limits";
    "Triangle Law" -> "Algebra of Limits";
    "Reverse Triangle Law" -> "Algebra of Limits";

    "Completeness of R" -> "Monotonic sequence converges iff bounded";
    "Approximation Property" -> "Monotonic sequence converges iff bounded";

    "Scenic Viewpoint Theorem" -> "Bolzano-Weierstrass Theorem";
    "Monotonic sequence converges iff bounded" -> "Bolzano-Weierstrass Theorem";

    "Triangle Law" -> "Cauchy convergence criterion";
 }