Mathematical analysis 1 term

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Mathematical analysis 1 term The distance course of higher mathematics NRNU MEPHI Mathematical analysis 1 term Lecture 1 Sets, numbers, mappings 11 of september 2014 year Lecturer: Docent of NRNU MEPHI, c.p.-m.s. Grishin Sergey Anatolyevich 1

Operations with sets

Algebra of sets 3

Example 4

Examples of formulas in algebra of sets 5

Real numbers 6

Axioms of real numbers 7

Consequences from axioms 8

Least upper, greatest lower bound 9

Theorems about sup and inf 10

Lemma about the embedded segments 11

Contractive segments 12

Mappings of sets 13

Injectiveness,surjectiveness,biuniqueness 14

Countability of Q 15

Uncountability of segment 16

Examples of mappings 17

Questions for examination 18

Thank you for за attention! The distance course of higher mathematics NRNU MEPHI Mathematical analysis. Sets, numbers, mappings. Lecture 1 Is completed. Thank you for за attention! Subject of the next lecture: Complex numbers. Lecture will be on Thursday 18 of september at 10-00 of the Moscow time. 19