## A Modern introduction to pure mathematics, Volume 1 |

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### Contents

LINGUISTIC CONCEPTS 1 Mathematics as a Language | 1 |

Constants | 3 |

Variables | 6 |

Copyright | |

28 other sections not shown

### Common terms and phrases

a a e absorptive laws aggregate anti-symmetric assignment of values axiom schema axiomatic theory bi-implication brackets Cartesian diagram composite concurrent constant deduce definition denotes domain e p a easily element equal equilateral equiv equivalence classes equivalence relation example expression F F F factor following theorem formal deduction formal language formation rules formula free occurrence free variables function given hypotheses Hence hypo hypotheses yield hypothesis infer integers interpretation intuitive logical axiom logically equivalent maps mathematical mathematical induction means meta-language natural numbers notion object language obtained obviously one-to-one ordered pairs p-relative partial ordering relation predicate prime number proof quantifier range consists reader reflexive required result follows result of exercise Rule Number schemata set-theory significant substitution Similarly simple ordering square symbols synonymous tautology transitive triangle truth-table truth-value value F variable whose range whilst