Foundations of Infinitesimal Calculus
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Foundations of Infinitesimal Calculus
Chapter 1. Numbers 3
1.1 Field Axioms 3
1.2 Order Axioms 6
1.3 The Completeness Axiom 7
1.4 Small, Medium and Large Numbers 9
Chapter 2. Functional Identities 17
2.1 Speci c Functional Identities 17
2.2 General Functional Identities 18
2.3 The Function Extension Axiom 21
2.4 Additive Functions 24
2.5 The Motion of a Pendulum 26
Chapter 1. Numbers 3
1.1 Field Axioms 3
1.2 Order Axioms 6
1.3 The Completeness Axiom 7
1.4 Small, Medium and Large Numbers 9
Chapter 2. Functional Identities 17
2.1 Speci c Functional Identities 17
2.2 General Functional Identities 18
2.3 The Function Extension Axiom 21
2.4 Additive Functions 24
2.5 The Motion of a Pendulum 26
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