intermediate value theorem

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(calculus) A theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.

日本語の意味

連続関数の像の最小上界と最大下界の間の任意の値に対して、その値をとる定義域上の対応する点が存在するという定理。

英語の意味

(calculus) A theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.

このボタンはなに？

When solving for a root of a continuous function on an interval, I used the intermediate value theorem to guarantee a zero exists between two points of opposite sign.

区間上の連続関数の根を求める際、連続関数が最小値と最大値の間の任意の値をとることを保証する定理（中間値の定理）を用いて、符号が異なる二点の間に零点が存在することを確認した。

詳細

意味（1）

(calculus) A theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.