Are Transcendental Numbers Countable?

Are Transcendental Numbers Countable? Are transcendental numbers countable? Since the real numbers are the union of algebraic and transcendental numbers, it is impossible for both subsets to be countable. This makes the transcendental numbers uncountable. No rational number is transcendental and all real transcendental numbers are irrational. Are transcendental numbers real numbers? A transcendental number