Almost All Real Numbers are Transcendental

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Almost all real numbers are transcendental.


By definition, a transcendental number (in this context) is a real number which is not an algebraic number.

Recall that the Real Numbers are Uncountable.

Also recall that the Algebraic Numbers are Countable.

Thus the subset of all real numbers which are not transcendental is countable.

The result follows by the definition of almost all.