The monsters and the critics and other essays online

These are the essential algebraic properties of groups, and they endow groups, like the set of symmetries of the square, with a structure and a regularity akin to those of our familiar number systems. Yet groups of symmetries also exhibit their own complex and subtle characteristics. For example, our group of symmetries of the square contains only eight elements, a stark contrast to our infinite number systems. And while we can combine symmetries in a manner similar to the way we add numbers, the order in which we combine them makes a difference: 3 + 4 = 4 + 3, but reflection followed by rotation is not necessarily the same as rotation followed by reflection.

The monsters and the critics and other essays online

the monsters and the critics and other essays online

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