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On real numbers, (aRb) if and only if (a-b\in Q). Which is the equivalence class of (\sqrt{2})?वास्तविक संख्याओं पर (aRb) तब और केवल तब जब (a-b\in Q)। (\sqrt{2}) का तुल्यता वर्ग कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ({\sqrt{2}+q:q\in Q})({\sqrt{2}+q:q\in Q})
Step 1: A number (x) is related to (\sqrt{2}) when (x-\sqrt{2}) is rational. Step 2: So (x=\sqrt{2}+q), where (q\in Q). Step 3: Classes based on rational difference contain infinitely many numbers, not just one number.चरण 1: (x) तभी (\sqrt{2}) से सम्बन्धित होगा जब (x-\sqrt{2}) परिमेय हो। चरण 2: इसलिए (x=\sqrt{2}+q), जहाँ (q\in Q)। चरण 3: परिमेय अंतर वाले वर्गों में अनन्त संख्याएँ होती हैं, केवल एक संख्या नहीं।
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