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What exactly is a partition, $P$, of a grid, $G,$ on a region, $R$, of $mathbbR^n$?
Where to go after Advanced Calculus 2?Nonobvious examples of metric spaces that do not work like $mathbbR^n$Possible Path in a 2D gridwhat do these complex analysis terms mean?Can you identify this book?What exactly is a derivative?Study Tips and Techniques for Self-Oriented StudentsShow that $f(z) = 5sin(z) - exp(z)$ has exactly one zero in a region.How to partition $mathbb Z times mathbb Z$?Proof partition
$begingroup$
I'm studying Jordan regions in analysis but because I don't have the text (I couldn't afford the book and can't find the pdf anywhere) I'm having trouble grasping one of the concepts. We learned about Jordan regions, $R$ on $mathbbR^n$ and how you can split them up with a Grid, $G$. However in my notes the professor briefly mentions partitions of $G$ and didn't elaborate much about it at all. Specifically he wrote that there are integers $v_j in mathbbN$ and partitions $P_j = P_j(G) = x^j_k $ of $[a_j,b_j]$ such that $G$ is the collection of rectangles $I_1 times cdots times I_n$ where each $I_j = [x^j_k-1,x^j_k]$ for some $k = 1, ldots , v_j$.
I would ask the professor directly but he typically doesn't like to explain things that are elaborated in the text has told me as much before. Also I thought it might not be that important until we covered a proof that used partitions in class today and I was honestly too afraid to ask him to explain partitions because of previous chastising for asking those sorts of questions. I have tried to google around for more information on Jordan regions but my google-fu is weak or it's not a popular topic in college maths. Any input is greatly appreciated!
p.s. the text I need but don't have is "An Introduction to Analysis" by Wade 4th edition
analysis
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add a comment |
$begingroup$
I'm studying Jordan regions in analysis but because I don't have the text (I couldn't afford the book and can't find the pdf anywhere) I'm having trouble grasping one of the concepts. We learned about Jordan regions, $R$ on $mathbbR^n$ and how you can split them up with a Grid, $G$. However in my notes the professor briefly mentions partitions of $G$ and didn't elaborate much about it at all. Specifically he wrote that there are integers $v_j in mathbbN$ and partitions $P_j = P_j(G) = x^j_k $ of $[a_j,b_j]$ such that $G$ is the collection of rectangles $I_1 times cdots times I_n$ where each $I_j = [x^j_k-1,x^j_k]$ for some $k = 1, ldots , v_j$.
I would ask the professor directly but he typically doesn't like to explain things that are elaborated in the text has told me as much before. Also I thought it might not be that important until we covered a proof that used partitions in class today and I was honestly too afraid to ask him to explain partitions because of previous chastising for asking those sorts of questions. I have tried to google around for more information on Jordan regions but my google-fu is weak or it's not a popular topic in college maths. Any input is greatly appreciated!
p.s. the text I need but don't have is "An Introduction to Analysis" by Wade 4th edition
analysis
$endgroup$
add a comment |
$begingroup$
I'm studying Jordan regions in analysis but because I don't have the text (I couldn't afford the book and can't find the pdf anywhere) I'm having trouble grasping one of the concepts. We learned about Jordan regions, $R$ on $mathbbR^n$ and how you can split them up with a Grid, $G$. However in my notes the professor briefly mentions partitions of $G$ and didn't elaborate much about it at all. Specifically he wrote that there are integers $v_j in mathbbN$ and partitions $P_j = P_j(G) = x^j_k $ of $[a_j,b_j]$ such that $G$ is the collection of rectangles $I_1 times cdots times I_n$ where each $I_j = [x^j_k-1,x^j_k]$ for some $k = 1, ldots , v_j$.
I would ask the professor directly but he typically doesn't like to explain things that are elaborated in the text has told me as much before. Also I thought it might not be that important until we covered a proof that used partitions in class today and I was honestly too afraid to ask him to explain partitions because of previous chastising for asking those sorts of questions. I have tried to google around for more information on Jordan regions but my google-fu is weak or it's not a popular topic in college maths. Any input is greatly appreciated!
p.s. the text I need but don't have is "An Introduction to Analysis" by Wade 4th edition
analysis
$endgroup$
I'm studying Jordan regions in analysis but because I don't have the text (I couldn't afford the book and can't find the pdf anywhere) I'm having trouble grasping one of the concepts. We learned about Jordan regions, $R$ on $mathbbR^n$ and how you can split them up with a Grid, $G$. However in my notes the professor briefly mentions partitions of $G$ and didn't elaborate much about it at all. Specifically he wrote that there are integers $v_j in mathbbN$ and partitions $P_j = P_j(G) = x^j_k $ of $[a_j,b_j]$ such that $G$ is the collection of rectangles $I_1 times cdots times I_n$ where each $I_j = [x^j_k-1,x^j_k]$ for some $k = 1, ldots , v_j$.
I would ask the professor directly but he typically doesn't like to explain things that are elaborated in the text has told me as much before. Also I thought it might not be that important until we covered a proof that used partitions in class today and I was honestly too afraid to ask him to explain partitions because of previous chastising for asking those sorts of questions. I have tried to google around for more information on Jordan regions but my google-fu is weak or it's not a popular topic in college maths. Any input is greatly appreciated!
p.s. the text I need but don't have is "An Introduction to Analysis" by Wade 4th edition
analysis
analysis
asked Mar 20 at 19:05
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