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Occasionally when trying to prove a certain type of object exists, it is easier to show that the set of those objects is very large. For instance, it's difficult to give an example of a transcendental number over the realsrationals. However, it is quite easy to show that the set of algebraic numbers is only countably infinite, so almost every real number is transcendental. |
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Occasionally when trying to prove a certain type of object exists, it is easier to show that the set of those objects is very large. For instance, it's difficult to give an example of a transcendental number over the reals. However, it is quite easy to show that the set of algebraic numbers is only countably infinite, so almost every real number is transcendental. |
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