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Chapter 01 - Real Number System @msc:real_analysis_notes_by_syed_gul_shah

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rline y\|=\|\underline x\| \|\underline y\|$. * Question: Suppose $\underline x,\underline y, \underline z... \,\underline y - \underline z \,} \right\|$. * Question: If //r// is rational and //x// is irrational then prove that $r+x$ and are $rx$ irrational. * Question: If //n// is a positive integer which is not perf... n prove that $\sqrt{n}$ is irrational number. * Question: Prove that $\sqrt{12}$ is irrational. * Questi

Chapter 04 - Differentiation @msc:real_analysis_notes_by_syed_gul_shah

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e Value Theorem or Darboux,s Theorem) * Related question * Riemann differentiation of vector valued func