At the foundations of any theory, there are truths, which are taken for granted and can't be proved or disproved. These are called axioms. The first axiomatic system was developed by Euclid in his boo...At the foundations of any theory, there are truths, which are taken for granted and can't be proved or disproved. These are called axioms. The first axiomatic system was developed by Euclid in his books called "Elements". The most basic terms of geometry are point, line, and plane. A point has no dimension (length or width), but it does have a location. A line is straight and extends infinitely in the opposite directions. A plane is a flat surface that extends indefinitely.
The reader who has seen group theory will know that in addition to the three properties listed in our definition, the group operation must satisfy a property called associativity. In the context of tr...The reader who has seen group theory will know that in addition to the three properties listed in our definition, the group operation must satisfy a property called associativity. In the context of transformations, the group operation is composition of transformations, and this operation is always associative. So, in the present context of transformations, we omit associativity as a property that needs checking.
