Sets

A set is a collection of well-defined objects. For example, a chair is an object and a collection of chairs is known as a set. Similarly the numbers 1, 2 and 3 individually are considered as objects, but collectively they form a set. A set can be defined by either making a list or by specifying some properties.

If an object x is in the list that defines a set S, then we say that x is a member or element of S or simply that x is in S.

There are some symbols for some predefined sets of numbers:

N: set of natural numbers

Z: set of integers

Q: set of rational numbers or fractions

R: set of real numbers

A set can be written as a following notation:

X={n∈N|n is an odd number}

This can be read as X is a set of all natural numbers n such that n is an odd number.

Similarly, set of all natural numbers which are multiple of 11 can be denoted as:

A={n∈N|n is a multiple of 11}

 

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