English Dictionary

without loss of generality

前置詞句

(mathematics) With a constraining assumption that, however, makes it clear how to apply the proof performed under this assumption to the general case unconstrained by the assumption.

日本語の意味

一般性を損なうことなく、特定の制約（仮定）のもとで証明や議論を展開し、その制約の仮定があっても結論が一般的に適用できることを示す表現。 / 数学的議論において、限定的な前提条件を採用するが、その前提条件に依存せず、最終的な結論が全体に当てはまることを意味する。

Without loss of generality, assume x ≤ y so that we can prove the inequality for this ordering and then extend it to all cases by symmetry.

一般性を損なうことなく x ≤ y と仮定すれば、この順序について不等式を証明し、対称性によりすべての場合に拡張できます。

意味（1）

(mathematics) With a constraining assumption that, however, makes it clear how to apply the proof performed under this assumption to the general case unconstrained by the assumption.

We wish to prove two ellipses in the plane intersect in an even number of points or are tangent. Without loss of generality, assume one of them has the equation x²+y²=1.