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In math, group theory is a branch of what is called "abstract algebra" that study special sets of objects called "groups".
Example: you may have studied the following facts about adding numbers.
1.) Every number has a negative of itself. (for any x there is a -x)
2.) Zero added to any number leaves that number the same. (x+0=x)
3.) No matter where you put the parentheses, addition turns out the same. For example, (x+y) +z = x+(y+z)
Therefore, numbers -- combined with the operation of addition -- form a "group" because of these three attributes.
If you learn group theory, you will discover that not just numbers obey these properties. Things like geometric symmetries, permutations, and matrices can all be described as belonging to groups.
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