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Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
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is the difference between rational and irrational numbers? - Is there a rational number exists between any two rational numbers. - Is there a real number exists between any two real numbers. - Is the set of rational numbers countable? - Is the set of real numbers countable? - Give an examp
Chapter 01 - Real Number System @msc:real_analysis_notes_by_syed_gul_shah
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property. * Field. * Proofs of axioms of real numbers. * Ordered field. * Theorems on ordered field... (a) Archimedean property (b) Between any two real numbers there exits a rational number. * Theorem: Given two real numbers //x// and //y//, $x<y$ there is an irrational num... al //y// such that $y^n=x$. * The extended real numbers. * Euclidean space. * Theorem: Let $\underlin
Chapter 02 - Sequence and Series @msc:real_analysis_notes_by_syed_gul_shah
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y Sequence * Theorem: A Cauchy sequence of real numbers is bounded. * Divergent Sequence * Theorem: I... $. * Theorem: Let //a// and //b// be fixed real numbers if $\{s_n\}$ and $\{t_n\}$ converge to //s// and ... uence $\left\{{r_n}\right\}$ of distinct rational numbers such that $\lim_{n\to \infty}{r_n}=x$. * Let a ... lation * Theorem: Every Cauchy sequence of real numbers has a convergent subsequence. * Theorem (Cauchy