10-327/Homework Assignment 5 - Revision history

Anne.d: EDIT: moved Kai's HW5 solutions to new page

2010-12-11T02:54:47Z

EDIT: moved Kai's HW5 solutions to new page

← Older revision		Revision as of 22:54, 10 December 2010
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	*Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai		*Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai
	** Indeed so, though usually when talking about boundedness, people use the letter <math>M</math> and not the letter <math>\epsilon</math>. It makes no difference, of course.		** Indeed so, though usually when talking about boundedness, people use the letter <math>M</math> and not the letter <math>\epsilon</math>. It makes no difference, of course.

	===Solution===
	[http://katlas.math.toronto.edu/drorbn/images/7/77/10-327a501.JPG page1]
	[http://katlas.math.toronto.edu/drorbn/images/7/7e/10-327a502.JPG page2]
	[http://katlas.math.toronto.edu/drorbn/images/6/6b/10-327a503.JPG page3]
	[http://katlas.math.toronto.edu/drorbn/images/6/61/10-327a504.JPG page4]
	[http://katlas.math.toronto.edu/drorbn/images/1/1d/10-327a505.JPG page5]
	[http://katlas.math.toronto.edu/drorbn/images/c/c6/10-327a506.JPG page6]
	[http://katlas.math.toronto.edu/drorbn/images/7/77/10-327a507.JPG page7]
	[http://katlas.math.toronto.edu/drorbn/images/d/df/10-327a508.JPG page8]
	[http://katlas.math.toronto.edu/drorbn/images/9/9d/10-327a509.JPG page9]
	[http://katlas.math.toronto.edu/drorbn/images/8/8e/10-327a510.JPG page10]
	[http://katlas.math.toronto.edu/drorbn/images/7/75/10-327a511.JPG page11]
	[http://katlas.math.toronto.edu/drorbn/images/7/70/10-327a512.JPG page12]
	[http://katlas.math.toronto.edu/drorbn/images/d/dc/10-327a513.JPG page13]
	[http://katlas.math.toronto.edu/drorbn/images/4/4d/10-327a514.JPG page14]
	[http://katlas.math.toronto.edu/drorbn/images/c/c5/10-327a515.JPG page15]
	[http://katlas.math.toronto.edu/drorbn/images/6/6d/10-327a516.JPG page16]
	[http://katlas.math.toronto.edu/drorbn/images/c/c6/10-327a517.JPG page17]
	[http://katlas.math.toronto.edu/drorbn/images/d/d5/10-327a518.JPG page18]

	An assignment without a solution is like a nightmare to me. I like every question accompanied
	with a clean solution aside.(Might not be the case for research question because they are just
	simply too hard.) I would like to share this happiness of understanding and acquiring knowledge
	with everybody because I don't think this class is a battle. I certainly don't like the idea that
	we should keep information/answers as something like business secrets. This learning process
	should be enjoyable which should be full of discussions instead of things like "you have to think on
	your own/ I can't tell you the answer". I know maybe other people might not agree with me but I believe
	a positive learning environment is crucial to truly understanding something well although we should not neglect
	independent thinking at the same time. That is why I share whatever I have with you. If I am wrong feel free to criticize
	me, and I am pretty sure a lot of people don't agree with me. But that is OK because there is just no
	absolute right or wrong and everybody is doing what they think is right. Just like you can't say if
	Axiom of choice is right or not. If you believe then it is right. If you don't believe it then it is wrong.
	Or maybe, for the entire subject--math, if you believe it then it is right. If you don't believe it then it
	is completely wrong.-Kai

Xwbdsb: /* Solution */

2010-11-20T01:28:12Z

Solution

← Older revision		Revision as of 21:28, 19 November 2010
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	An assignment without a solution is like a nightmare to me. I like every question accompanied		An assignment without a solution is like a nightmare to me. I like every question accompanied
	with a clean solution ~~beside~~.(Might not be the case for research question because they are just		with a clean solution aside.(Might not be the case for research question because they are just
	simply too hard.) I would like to share this happiness of understanding and acquiring knowledge		simply too hard.) I would like to share this happiness of understanding and acquiring knowledge
	with everybody because I don't think this class is a battle. I certainly don't like the idea that		with everybody because I don't think this class is a battle. I certainly don't like the idea that

Xwbdsb: /* Solution */

2010-11-20T01:24:24Z

Solution

← Older revision		Revision as of 21:24, 19 November 2010
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	should be enjoyable which should be full of discussions instead of things like "you have to think on		should be enjoyable which should be full of discussions instead of things like "you have to think on
	your own/ I can't tell you the answer". I know maybe other people might not agree with me but I believe		your own/ I can't tell you the answer". I know maybe other people might not agree with me but I believe
	a positive learning environment is crucial to truly ~~learn~~ something well although we should not neglect		a positive learning environment is crucial to truly understanding something well although we should not neglect
	independent thinking. That is why I share whatever I have with you. If I am wrong feel free to criticize		independent thinking at the same time. That is why I share whatever I have with you. If I am wrong feel free to criticize
	me, and I am pretty sure a lot of people don't agree with me. But that is OK because there is just no		me, and I am pretty sure a lot of people don't agree with me. But that is OK because there is just no
	absolute right or wrong and everybody is doing what they think is right. Just like you can't say if		absolute right or wrong and everybody is doing what they think is right. Just like you can't say if

Xwbdsb: /* Solution */

2010-11-20T01:23:43Z

Solution

← Older revision		Revision as of 21:23, 19 November 2010
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	simply too hard.) I would like to share this happiness of understanding and acquiring knowledge		simply too hard.) I would like to share this happiness of understanding and acquiring knowledge
	with everybody because I don't think this class is a battle. I certainly don't like the idea that		with everybody because I don't think this class is a battle. I certainly don't like the idea that
	we should keep information/answers as something like business ~~secretes~~. This learning process		we should keep information/answers as something like business secrets. This learning process
	should be enjoyable which should be full of discussions instead of things like "you have to think on		should be enjoyable which should be full of discussions instead of things like "you have to think on
	your own/ I can't tell you the answer". I know maybe other people might not agree with me but I believe		your own/ I can't tell you the answer". I know maybe other people might not agree with me but I believe

Xwbdsb: /* Solution */

2010-11-20T01:23:12Z

Solution

← Older revision		Revision as of 21:23, 19 November 2010
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	[http://katlas.math.toronto.edu/drorbn/images/c/c6/10-327a517.JPG page17]		[http://katlas.math.toronto.edu/drorbn/images/c/c6/10-327a517.JPG page17]
	[http://katlas.math.toronto.edu/drorbn/images/d/d5/10-327a518.JPG page18]		[http://katlas.math.toronto.edu/drorbn/images/d/d5/10-327a518.JPG page18]

			An assignment without a solution is like a nightmare to me. I like every question accompanied
			with a clean solution beside.(Might not be the case for research question because they are just
			simply too hard.) I would like to share this happiness of understanding and acquiring knowledge
			with everybody because I don't think this class is a battle. I certainly don't like the idea that
			we should keep information/answers as something like business secretes. This learning process
			should be enjoyable which should be full of discussions instead of things like "you have to think on
			your own/ I can't tell you the answer". I know maybe other people might not agree with me but I believe
			a positive learning environment is crucial to truly learn something well although we should not neglect
			independent thinking. That is why I share whatever I have with you. If I am wrong feel free to criticize
			me, and I am pretty sure a lot of people don't agree with me. But that is OK because there is just no
			absolute right or wrong and everybody is doing what they think is right. Just like you can't say if
			Axiom of choice is right or not. If you believe then it is right. If you don't believe it then it is wrong.
			Or maybe, for the entire subject--math, if you believe it then it is right. If you don't believe it then it
			is completely wrong.-Kai

Xwbdsb: /* Due date */

2010-11-20T01:09:34Z

Due date

← Older revision		Revision as of 21:09, 19 November 2010
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	*Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai		*Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai
	** Indeed so, though usually when talking about boundedness, people use the letter <math>M</math> and not the letter <math>\epsilon</math>. It makes no difference, of course.		** Indeed so, though usually when talking about boundedness, people use the letter <math>M</math> and not the letter <math>\epsilon</math>. It makes no difference, of course.

			===Solution===
			[http://katlas.math.toronto.edu/drorbn/images/7/77/10-327a501.JPG page1]
			[http://katlas.math.toronto.edu/drorbn/images/7/7e/10-327a502.JPG page2]
			[http://katlas.math.toronto.edu/drorbn/images/6/6b/10-327a503.JPG page3]
			[http://katlas.math.toronto.edu/drorbn/images/6/61/10-327a504.JPG page4]
			[http://katlas.math.toronto.edu/drorbn/images/1/1d/10-327a505.JPG page5]
			[http://katlas.math.toronto.edu/drorbn/images/c/c6/10-327a506.JPG page6]
			[http://katlas.math.toronto.edu/drorbn/images/7/77/10-327a507.JPG page7]
			[http://katlas.math.toronto.edu/drorbn/images/d/df/10-327a508.JPG page8]
			[http://katlas.math.toronto.edu/drorbn/images/9/9d/10-327a509.JPG page9]
			[http://katlas.math.toronto.edu/drorbn/images/8/8e/10-327a510.JPG page10]
			[http://katlas.math.toronto.edu/drorbn/images/7/75/10-327a511.JPG page11]
			[http://katlas.math.toronto.edu/drorbn/images/7/70/10-327a512.JPG page12]
			[http://katlas.math.toronto.edu/drorbn/images/d/dc/10-327a513.JPG page13]
			[http://katlas.math.toronto.edu/drorbn/images/4/4d/10-327a514.JPG page14]
			[http://katlas.math.toronto.edu/drorbn/images/c/c5/10-327a515.JPG page15]
			[http://katlas.math.toronto.edu/drorbn/images/6/6d/10-327a516.JPG page16]
			[http://katlas.math.toronto.edu/drorbn/images/c/c6/10-327a517.JPG page17]
			[http://katlas.math.toronto.edu/drorbn/images/d/d5/10-327a518.JPG page18]

Drorbn at 21:53, 3 November 2010

2010-11-03T21:53:28Z

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	{{Template:10-327:Dror/Students Divider}}		{{Template:10-327:Dror/Students Divider}}

		⚫	*Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai
	*Question.
			** Indeed so, though usually when talking about boundedness, people use the letter <math>M</math> and not the letter <math>\epsilon</math>. It makes no difference, of course.
⚫	in 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai

Xwbdsb: /* Due date */

2010-11-03T02:35:22Z

Due date

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	{{Template:10-327:Dror/Students Divider}}		{{Template:10-327:Dror/Students Divider}}

			*Question.
			in 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? -Kai

Drorbn at 01:06, 2 November 2010

2010-11-02T01:06:17Z

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	{{10-327/Navigation}}		{{10-327/Navigation}}
	{{In Preparation}}

	===Reading===		===Reading===
	Read sections 26 and 27 in Munkres' textbook (Topology, 2nd edition). Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, '''preread''' sections 28 and 29, just to get a feel for the future.		'''Read''' sections 26 and 27 in Munkres' textbook (Topology, 2nd edition). Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, '''preread''' sections 28 and 29, just to get a feel for the future.

	===Doing===		===Doing===

Drorbn at 15:13, 1 November 2010

2010-11-01T15:13:33Z

← Older revision		Revision as of 11:13, 1 November 2010
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	===Doing===		===Doing===
	Solve the following problems from Munkres' book, though submit only the <u>underlined</u> ones: Problems ?? on ~~page~~ ~~???~~, and ~~problems~~ ?? on ~~pages~~ ~~???~~.		Solve the following problems from Munkres' book, though submit only the <u>underlined</u> ones: Problems 1, <u>4</u>, <u>5</u>, 6, <u>7</u>, 8, <u>9</u>, 12 on pages 170-172, and problem <u>2</u> on page 177. (For the last, recall that <math>d(x,A):=\mbox{inf}_{a\in A}d(x,a)</math>).

	===Due date===		===Due date===