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MTH321: Real Analysis I (Spring 2023)

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om Chapter 02** - A convergent sequence of real number has one and only one limit (i.e. limit of the seq... }$ also converges to $s$. - For each irrational number $x$, there exists a sequence $\left\{ {{r}_{n}} \right\}$ of distinct rational numbers such that $\underset{n\to \infty }{\mathop{\lim... _{n}}}$ is convergent if and only if for any real number $\varepsilon >0$, there exists a positive integer

MTH322: Real Analysis II (Spring 2023)

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erentiation, integration, sequences and series of numbers, that is many notions included in [[atiq:fa21-mt... exists a convergent series $\sum M_n$ of positive numbers such that for all $x\in [a,b]$ $\left|f_n(x)\rig... third part will be related to application of the theory. **Questions from Chapter 01:** - Suppose that... exists a convergent series $\sum M_n$ of positive numbers such that for all $x\in [a,b]$ $\left|f_n(x)\rig