A set is a group of things, ex: {dog, food}
A subset is a set that has only things also in the super set, examples: {dog}, {food}, {dog, food}
A power set is the set of all subsets, ex: {(dog), (food), (dog, food)}.
It follows that the number of things of things in a subset is less than or equal to its parent set, which is in turn less than the number in its power set.
...prepare for mindlblowing...
Suppose there is a set of all things called the universe, then any set must be a subset of the universe. But this implies that the power set is a subset of the universe, which is a logical contradiction since the power set is larger than the universe. Thus, the universe doesn't exist.
A subset is a set that has only things also in the super set, examples: {dog}, {food}, {dog, food}
A power set is the set of all subsets, ex: {(dog), (food), (dog, food)}.
It follows that the number of things of things in a subset is less than or equal to its parent set, which is in turn less than the number in its power set.
...prepare for mindlblowing...
Suppose there is a set of all things called the universe, then any set must be a subset of the universe. But this implies that the power set is a subset of the universe, which is a logical contradiction since the power set is larger than the universe. Thus, the universe doesn't exist.
No comments:
Post a Comment