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- 13:15, 11 November 2025 CRN 10459: HW 6 (hist) [1,499 bytes] HelmutKnaust (Talk | contribs) (Created page with "'''Problem 26.''' Let $f,g:\mathbb{R}\to\mathbb{R}$ be two continuous functions. Define $h(x)=\max\{f(x),g(x)\}$ for all $x\in\mathbb{R}$. Show that $h$ is continuous on $\ma...")
- 11:32, 11 November 2025 CRN 10459: Final Projects (hist) [2,747 bytes] HelmutKnaust (Talk | contribs) (Created page with "*The final project will account for 25% of your course grade. *Groups of three students each will work on one of the final projects. *Deliverables consist of a 10-minute pr...")
- 15:36, 27 October 2025 CRN 10459: HW 5 (hist) [1,396 bytes] HelmutKnaust (Talk | contribs) (Created page with "'''Problem 21.''' Two Cauchy sequences $(a_n)$ and $(b_n)$ are said to be equivalent if $\lim_{n\to\infty} |a_n-b_n|=0$. Show that this indeed defines an equivalence relation ...")
- 09:46, 14 October 2025 CRN 10459: HW 4 (hist) [563 bytes] HelmutKnaust (Talk | contribs) (Created page with "'''Problem 16.''' Show: If $X\subseteq \mathbb{R}$ is both open and closed, then $X=\mathbb{R}$ or $X=\emptyset$. '''Problem 17.''' Exercise 3.2.7. '''Problem 18.''' Exercis...")
- 09:37, 30 September 2025 CRN 10459: HW 3 (hist) [1,117 bytes] HelmutKnaust (Talk | contribs) (Created page with "'''Problem 11.''' Suppose $(a_n)$ is a Cauchy sequence, and that $(b_n)$ is a sequence satisfying $\lim_{n\to\infty} |a_n-b_n|=0$. Show that $(b_n)$ is a Cauchy sequence. '''...")
- 10:25, 15 September 2025 CRN 10908 (hist) [56 bytes] HelmutKnaust (Talk | contribs) (Created page with "The course is completely online - see Blackboard Ultra.")
- 10:11, 15 September 2025 CRN 10459: HW 2 (hist) [1,052 bytes] HelmutKnaust (Talk | contribs) (Created page with "'''Problem 6.''' Using the limit definition, show that the sequence $(a_n)_{n=1}^\infty$, given by \[a_n=\sqrt{\frac{2n+5}{n+2}}\] converges to $\sqrt{2}$. '''Problem 7.''' ...")
- 18:24, 29 August 2025 CRN 10459: HW 1 (hist) [1,079 bytes] HelmutKnaust (Talk | contribs) (Created page with "'''Problem 1.''' Let $A$ and $B$ be two non-empty sets that are bounded from above. Show: If $\sup A < \sup B$, then $B$ contains an element that is an upper bound of $A$. ''...")
