**
Basic notions. Examples of sets
**

*
Set.
*
*
Element of a set.
Finite set.
Empty set.
*

*
Infinite set. Countable set.
*
*
Uncountable set.
*

*
Convex set. Methods of
description of sets.
*

**
**

**
A set
**
and

**concern with category of**

*an element of a set**primary notions*, for which it's impossible to formulate the strict definitions. So, we imply as sets usually collections of objects ( elements of a set ), having certain common properties. For instance, a set of books in a library, a set of cars on a parking lot, a set of stars in the sky, a world of plants, a world of animals – these are examples of sets.

**
A finite set
**
consists of finite number of
elements, for example,
a set of pages in a book, a set of
pupils in a school etc.

**
An empty set
**
(
its
designation is
)

**doesn't contain any elements, for instance, the set of winged elephants, the set of roots of the equation sin**

*x*= 2 etc.

**
An infinite set
**
consists of infinite number of
elements, i.e. this is a set, which isn't finite and empty.
Examples: the set
of real numbers,
a set of points
on a plane,
a set of atoms in the
universe etc.

**
A countable set
**
is a set, elements
of which can be numbered.
For example,
the sets of natural, even,
odd numbers. A countable set can be finite ( a set of books in a library ) or
infinite ( the set of integers, its elements can be numbered as follows:

*
the set elements:
*
…, –5, – 4, –3, –2, –1, 0, 1, 2, 3, 4, 5, …

*
their numbers:
*
… 11 9 7
5 3 1 2 4 6 8 10 … ) .

**
An uncountable set
**
is a set, elements of which
can't be numbered.
For
example,
the set of real numbers. An uncountable set can be only infinite (
think,
please,
why
?
).

**
A convex set
**
is a set, which for any two its
points

*A*and

*B*contains also the whole segment

*AB*. Examples of convex sets: a straight line, a plane, a circle. But a circumference is not a convex set.

**
**

**
Methods of description of sets
**

*.*A set can be described the following ways:

– an enumeration of all its elements by theirs names ( for example, a set of books in a library, a set of pupils in a class, an alphabet of any language and so on );

– by giving of common performance (common properties) of elements of the set ( for instance, the set of rational numbers, the family of dogs, the family of cats etc.);

– formal law of forming elements of the set ( for example, the formula of a general term of numerical sequence, Periodic table of chemical elements ).