1.
theorem; established mathematical or logical truth
A statement in mathematics or logic that has been proven to be true through rigorous logical reasoning from axioms and previously established results.
定理を証明する。
To prove a theorem.
ピタゴラスの定理は有名だ。
The Pythagorean theorem is famous.
この定理は数学の多くの分野で応用されている。
This theorem is applied in many fields of mathematics.
Composed of 定 (established/fixed) and 理 (principle/logic). The fundamental unit of proven knowledge in mathematics and formal logic.
COMMON COLLOCATIONS:
- 定理を証明する: to prove a theorem
- 定理を応用する: to apply a theorem
- ピタゴラスの定理: the Pythagorean theorem
- 二項定理: the binomial theorem
- 中間値の定理: the intermediate value theorem
SIMILAR WORDS:
- 公理: axiom — a statement accepted as true without proof, serving as a starting point
- 法則: law / rule — a general principle, especially in natural sciences (e.g., Newton's laws)
- 公式: formula — a mathematical expression or equation, not a proven statement
- 命題: proposition — a statement that may or may not be proven, broader than 定理