24
edits
Changes
Jump to navigation
Jump to search
Line 6:
Line 6: + +
no edit summary
The easiest way to prove the existence of [[transcendental]] numbers is by a nonconstructive proof, arguing that the set of [[real number]]s is [[uncountable]] while the set of [[algebraic number]]s is [[countable]], and thus (many) transcendental numbers must exist. Of course, finding a specific example is a much more difficult endeavor.
The easiest way to prove the existence of [[transcendental]] numbers is by a nonconstructive proof, arguing that the set of [[real number]]s is [[uncountable]] while the set of [[algebraic number]]s is [[countable]], and thus (many) transcendental numbers must exist. Of course, finding a specific example is a much more difficult endeavor.
Of course, nonconstructive proofs are the only way to prove many theorems in mathematics such as the uncountability of the real numbers or the insolvability of the general quintic.
[[Category:mathematics]]
[[Category:mathematics]]