Binary Operations

The things missed in Mathematics!

1.       I like to travel a lot.

2.       See the map of Bangalore city below (Courtesy: Google Maps).

3.       You can see an intersection of roads circled.

4.       If you are coming from North to South, then this junction is simply a Binary Operation.

5.       The two roads belong to Bangalore City Roads (a Set).

6.       And these two roads combine to give another road that also belong to Bangalore City Roads.

Few formalized representations:

A binary operation on a set A is defined as a function from AxA to A. That is to mean, if you take any two elements from A and apply the binary operation, you will get another element from A.

For example, addition (+) on set of Natural numbers* is a binary operation (addition of two natural numbers gives us another natural number).

But, subtraction (-) on set of Natural numbers is not a binary operation (subtraction of two numbers can be negative, and negative numbers are not Natural numbers.

*Natural numbers are counting numbers, starting from 1,2,3,4,…