Concept explainers
(a) A real number
with rational coefficients
(b) A real number is said to be transcendental if it is not algebraic. Assuming the reals are uncountable, show that the transcendental numbers are uncountable. (It is a somewhat surprising fact that only two transcendental numbers are familiar to us:
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Topology
- 13. Prove that if and are rational numbers such that then there exists a rational number such that . (This means that between any two distinct rational numbers there is another rational number.)arrow_forwardOne of the zeros is given for each of the following polynomial. Find the other zeros in the field of complex numbers. is a zero. is a zero. is a zero is a zero.arrow_forward
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