Exercise 3.1 Solution: Let $\e=0.001$. Because $(a_n)$ converges to $0.001$, there exist $N$ such that for all $n> N$ we have\[|a_n-0.001| < 0.001,\]\[\Longrightarrow -0.001 < a_n- 0.001 < 0.001,\]\[\Longrightarrow 0<…
Exercise 1.8 Solution: (a) Because $a < b$, we have $b-a\in P$. Similarly, we have $d-c\in P$. We have\begin{align*}(b+d)-(a+c)&=b+d-a-c\\ \text{ by Axiom 6 (a)} \quad&=(b-a)+(d-c)\in P.\end{align*}Hence $a+c < b+d$. (b)…
Please feel free to submit your solutions by comments. It supposrts LaTeX vis Mathjax! Here is my motivation to do this! Chapter 1 The Reals #1, #2, #3, #4, #5,…
Chapter 10 Integration of Differential Forms Exercise 2 (By analambanomenos) The $\varphi_i(x)\varphi_i(y)$ has support in the square $2^{-i}<x<2{-1+1}$, $2^{-i}<y<2{-1+1}$, and the $\varphi_{i+1}(x)\varphi_i(y)$ term has support in the rectangle $2^{-i-1}<x<2{-1}$, $2^{-i}<y<2{-1+1}$,…
Chapter 9 Functions of Several Variables Part A: Exercise 1 - Exercise 12 Part B: Exercise 13 - Exercise 22 Part C: Exercise 23 - Exercise 31 Exercise 23 (By…
Chapter 9 Functions of Several Variables Part A: Exercise 1 - Exercise 12 Part B: Exercise 13 - Exercise 22 Part C: Exercise 23 - Exercise 31 Exercise 13 (By…
Chapter 9 Functions of Several Variables Part A: Exercise 1 - Exercise 12 Part B: Exercise 13 - Exercise 22 Part C: Exercise 23 - Exercise 31 Exercise 1 (By…
Chapter 8 Some Special Functions Part A: Exercise 1 - Exercise 12 Part B: Exercise 13 - Exercise 20 Part C: Exercise 21 - Exercise 31 Exercise 21 (By analambanomenos)…
Chapter 8 Some Special Functions Part A: Exercise 1 - Exercise 12 Part B: Exercise 13 - Exercise 20 Part C: Exercise 21 - Exercise 31 Exercise 13 (By analambanomenos)…
Chapter 8 Some Special Functions Part A: Exercise 1 - Exercise 12 Part B: Exercise 13 - Exercise 20 Part C: Exercise 21 - Exercise 31 Exercise 1 (By Matt…