Prove that the set T of transcendental numbers (numbers that do not satisfy some polynomial equation of positive degree with rational coefficients) has the power of the continuum, i.e. has cardinality c.(adsbygoogle = window.adsbygoogle || []).push({});

Here's what I have: Since T is uncountable, then |T|>alephnull . Also, since T is a subset of R , then |T| not> c . Thus, by the Continuum Hypothesis, we must have |T|=c .

But is there a way to get a proof without using the Continuum Hypothesis, by showing directly a bijection between T and R?

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# Homework Help: Prove that the set of transcendental numbers has cardinality c

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