## ⓘ Intermediate value theorem

The intermediate value theorem says that if a function, f {\displaystyle f}, is continuous over a closed interval }, and is equal to f {\displaystyle f} and f {\displaystyle f} at either end of the interval, for any number, c, between f {\displaystyle f} and f {\displaystyle f}, we can find an x {\displaystyle x} so that f = c {\displaystyle f=c}.

This means that if a continuous functions sign changes in an interval, we can find a root of the function in that interval. For example, if f 1 = − 1 {\displaystyle f1=-1} and f 2 = 2 {\displaystyle f2=2}, we can find an x {\displaystyle x} in the interval } that is a root of this function, meaning that for this value of x, f x = 0 {\displaystyle fx=0}, if f {\displaystyle f} is continuous. This corollary is called Bolzanos theorem.

- other intermediate values from key generation. Although this form allows faster decryption and signing by using the Chinese Remainder Theorem CRT it

Angle |

Mathematics |

0.999. |

4 (number) |

Absolute value |

Aleph null |

Aleph one |

Algebraic geometry |

Algebraic topology |

Algebraic variety |

Algorithmic information theory |

Alphabet (computer science) |

American Mathematical Society |

Applied mathematics |

Argument |

Arithmetic precision |

Associativity |

Automaton |

Average |

Axiom |

Babylonian numerals |

Banach–Tarski paradox |

Base (mathematics) |

Base ten block |

Bayes theorem |

Bayesian network |

Big O notation |

Binary |

Binary adder |

Binary operation |

Binomial expansion |

Bezier curve |

Canonical form |

Cantors theorem |

Category theory |

Cellular automaton |

Chaos theory |

Charge conjugation |

Clay Mathematics Institute |

Closure (mathematics) |

Combination (mathematics) |

Combinatorics |

Commutative property |

Complex analysis |

Complexity class |

Constructive proof |

Continuous function |

Contraposition |

Coordinate system |

Coprime |