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Finite Group
In the previous post, we look at a mathematical entity called Group.
Among all the groups, we are interested in finite groups. The order of a group is the cardinality of its underline set. A cardinality is the number of elements in a set. A finite group is a group whose order is finite.
An example is a tuple of a set of {True, False} and the logical xor operator. The logical xor operator takes two values and returns True only if two elements are different. The order of this group is 2. An identity element is False. An inverse of True is True. An inverse of False is False. The set is closed under the operation. Do you think that a set of {True, False} and the logical and operation is a group? How about {True, False} and the logical operation?
The most important reason why we are interested in finite groups is that we can write computer programs for almost everything.
We will use Python computer programming language. Python is very popular in data science, machine learning communities, computer science education. Recently Google provides Jupiter notebook for Python programming environment. So we can easily write and run Python programs without any complex setup.
