1.4

Glossary

Glossary

We are planning to prepare a Glossary for the course that contains a list of the key terms that are used in the course.

Which terms would you like us to explain here?

Symbols

$$:=$$ Equal by definition. E.g., for any real number $$a\in \mathbb R$$ one has $$a^2:= a\cdot a$$.

$$\exists$$ :There exists.

$$\in$$: Belongs to

$$\subset$$: Is a subset of

$$\cup$$: Union of sets

$$\cap$$: Intersection of sets

$$\forall$$: For every

$$\mathbb N$$: The set of natural numbers $$0,1,2,3,…$$.

$$\mathbb Q$$: The set of rational numbers.

$$\mathbb R$$: The set of real numbers.

$$\mathbb Z$$: The set of integer numbers $$…,-3,-2,-1,0, 1,2,3,…$$: $$\mathbb N\subset\mathbb Z\subset\mathbb Q\subset\mathbb R$$

I

Integer: a number of the set $$\mathbb Z=\lbrace …,-3,-2,-1,0,1,2,3,…\rbrace$$

N

Natural number: a number of the set $$\mathbb N=\lbrace 0,1,2,3,…\rbrace$$

R

Rational number: a number of the set $$\mathbb Q=\left\lbrace \dfrac ab:\, a\in\mathbb Z, b\in\mathbb Z\setminus\lbrace 0\rbrace\right\rbrace=\left\lbrace \dfrac ab:\, a\in\mathbb Z, b\in\mathbb N\setminus\lbrace 0\rbrace\right\rbrace$$

Real number: an element of $$\mathbb R$$. The set $$\mathbb R$$ contains the limits of sequences of rational numbers and elements like square roots, $$\pi, e,…$$

S

Square root of $$x\ge 0$$: the positive number $$y$$ satisfying $$y^2=x$$.

$$m-$$th root of $$x\ge 0$$: the positive number $$y$$ satisfying $$y^m=x$$.