Axioms of Real Numbers | Part 1: Field Axioms | Real Analysis | Lecture 1 скачать в хорошем качестве

Axioms of Real Numbers | Part 1: Field Axioms | Real Analysis | Lecture 1

This is the first lecture in the series of lectures on Real Analysis. It covers the field axioms satisfied by the real numbers and the properties that follow from these axioms. Other axioms of real numbers will be covered in subsequent videos. 0:00 Quantor notation 5:33 Axioms of real numbers 6:08 Definition of a field 11:44 Example: Are N, Z, Q fields? 13:20 Remarks on field notation, the definition of a subfield 14:06 A theorem that states properties of a field derived from field axioms 17:50 Proof of the uniqueness of additive identity in a field 20:07 Proof of the uniqueness of additive inverse of an element in a field 22:57 Proof of the statement that multiplying an element in a field by zero gives zero All lectures in Real Analysis: Real ANALYSIS -- Modern ANALYSIS -- Advanced CALCULUS    • Real ANALYSIS -- Modern ANALYSIS -- Advanc...