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Which statement is always true about two distinct irrational numbers on the number line?संख्या रेखा पर दो भिन्न अपरिमेय संख्याओं के बीच कौन-सा कथन सदैव सत्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: There is at least one rational number between themउनके बीच कम-से-कम एक परिमेय संख्या होती है
If \(x<y\), choose \(n\) such that \(1/n<y-x\); then some \(m/n\) lies between them. Hence A is correct. D is false because irrationals also lie between them. Exam tip: both sets are dense.यदि \(x<y\), तो \(1/n<y-x\) वाला \(n\) लेने पर कोई \(m/n\) इनके बीच मिलता है। इसलिए A सही है। D गलत है, क्योंकि बीच में अपरिमेय भी होते हैं। टिप: परिमेय और अपरिमेय दोनों सघन हैं।
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