## A bridge to advanced mathematics |

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### Contents

STARTING POINTS | 3 |

Logic Language and Mathematics | 9 |

Logic and Symbolic Logic | 11 |

Copyright | |

57 other sections not shown

### Common terms and phrases

abstract algebraic assumptions axiom of choice axiom system axiomatic calculus called Cantor's cardinal number chapter claim closed collection compact completeness axiom concept connected set connectedness consider consisting continuous function contradiction correspondence countable countable set defined Definition denote denumerable discussion equivalence relation Euclidian Euclidian geometry example existence finite geometry given idea implies induction infinite sets infinity integer interpretation intuitive Lemma limit point logically equivalent mathe mathematical thought mathematicians matics matter meaning method natural numbers negation neighborhood non-empty notation number system open interval open set parallel postulate point set precise problem propositional function Question rational numbers reader real numbers reason relative topology result Russell paradox same-number of elements sense sequence set theory statement subset Suppose supremum symbol things tion topological space true truth-value uncountable undefined upper bound usual topology words