Are you sure you know everything about sets?

Here’s a checklist!

1. Definition

A Set is a collection of things that have common properties.

Let us say for eg. - Set of even numbers: {..., -4, -2, 0, 2, 4,...}Set of odd numbers: {..., -3, -1, 1, 3, ...}Set of prime numbers: {2, 3, 5, 7, 11, 13, 17, ...}Positive multiples of 3 that are less than 10: {3, 6, 9}

2. Why are Sets Important?

The Set theory is a fundamental concept of mathematics.Sets are of no use as an individual concept. It gains recognition and become powerful building block of mathematics only when applied in different situations like Graph Theory, Abstract Algebra, Real Analysis, Complex Analysis, Linear Algebra, Number Theory, and so on.

3. Universal Set

A universal set is a set that contains everything including itself.

4. Representation

In Sets, it is an accepted custom to use Capital letters to represent the entire set and Small letters to represent the elements of the Set.

5. Subsets

A portion of a set that forms a set is a subset. To be called a subset, a set has to be the member of a bigger set.

A is a subset of B iff every element of A is in B.

6. Proper Subsets

A proper subset is a subset of a set if and only if every element in the subset is also in the set, and there exists at least one element in the set that is not in the subset.

7. Null Set or Empty Set

This is probably the weirdest thing about sets.There are no elements in an Null Set. It is represented by Or by {} (a set with no elements)

8. Null Set and Subsets

The Null Set is a subset of every set, including the Null Set itself.

9. Order

In sets it does not matter what order the elements are in.Example: {a, b, c, d) is the same set as {c, a, d, b}Order of a set implies the size of the set.Example, {1, 2, 3, 4} has an order of 4

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