Introduction to mathematics, issue 2

Subject Introduction to mathematics, taught at the first year of mathematics and IT studies at universities and technical colleges, due to its abstract nature is a novelty for new students. It contains content that often seems difficult at first, because they are different from those taught at school, but after understanding they are fascinating.
The author, referring repeatedly to the reader's intuition, introduces us in the accessible world to the world of collections (countable, uncountable), quantifiers, functions, relations and gradually introduces the formalization of the theory and language of mathematics. Numerous comments and interesting, carefully selected examples make it easier to absorb material. The tasks at the end of the chapters and the answers and hints for them make it possible to check the knowledge gained.

Table of Contents

Preface

A. Introduction to the entrance

l. The propositional calculus

L.1. Basic concepts
1.2. Tautologies and evidence
1.3. Important laws of the propositional calculus
1.4. Works

2. Collections

2.1. What is a collection?
2.2. Activities on collections
2.3. Properties of activities on sets
2.4. Works

3. Quantifiers

3.1. Basic concepts
3.2. The laws of the quantifier's account
3.3. A few words about the proofs
3.4. Generalized activities on sets
3.5. Works

4. Mathematical induction and recursion

4.l. Mathematical induction
4.2. recursion
4.3. Works

5. Functions

5.l. The concept of function
5.2. Properties of the function
5.3. Paintings and counterparts
5.4. Works

6. Relationships

6.1. The concept of relationship
6.2. Properties of the relationship
6.3. Equivalence relations
6.4. Relations of order
6.5. Works

7. Equilibrium of sets

7.1. Equal collections
7.2. Non-parallel sets
7.3. Comparing the harvesting power
7.4. Works

8. Countable and uncountable sets

8.1. Basic concepts
8.2. Countable sets
8.3. Sets of continuum power
8.4. Works

9. Some more difficult evidence

10. Answers and task tips

Additives

A. Axioms of set theory
B. Ordinal numbers
C. Cardinal numbers

Bibliography
Skrowidz