DS102

branch of mathematics involving discrete elements that uses algebra and arithmetic,  increasingly being applied in the practical fields of mathematics and computer science. It is a very good tool for improving reasoning and problem-solving capabilities.

German mathematician introduced the concept of sets. He had defined a set as a collection of definite and distinguishable objects selected by the means of certain rules or description.

forms the basis of several other fields of study like counting theory, relations, graph theory and finite state machines.

an unordered collection of different elements, can be written explicitly by listing its elements using set bracket. If the order of the elements is changed or any element of a set is repeated, it does not make any changes in the set.

set is represented by listing all the elements comprising it. The elements are enclosed within braces and separated by commas

set is defined by specifying a property that elements of the set have in common. The set is described as A={x:p(x)}

a measure of the "number of elements" of the set

Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between the different types of infinity, and to perform arithmetic on them

two approaches to cardinality

set has an infinite number of elements, its cardinality is