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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.
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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.
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Related words
without loss of generality
Prepositional phrase
Japanese Meaning
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。
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