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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.

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.

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 rationals. 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.