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By the intermediate value theorem, there is an angle [theta] [member of][[[theta].
com Now in an updated and expanded third edition, "A Concise Introduction To Pure Mathematics" by Martin Liebeck provides an informed and informative presentation into a representative selection of fundamental ideas in mathematics including the theory of solving cubic equations, the use of Euler's formula to study the five Platonic solids, the use of prime numbers to encode and decode secret information, the theory of how to compare the sizes of two infinite sets, the limits of sequences and continuous functions, the use of the intermediate value theorem to prove the existence of nth roots, and so much more.
This can be proven by supposing that g (a) [greater than or equal to] a and g(b) [less than or equal to] b that is (a [greater than or equal to] [a, b] [less than or equal to] b ) = g (a) - a [greater than or equal to] a and g(b) - b [greater than or equal to] 0 Since g is continuous, the intermediate value theorem guarantees that there exist c [member of] [a, b] such that g(c) - c =0 so there must exist a 'c' such that g(c) = c This means that there must exist a fixed point [member of] [a, b] Example 2.