Talk:06-240/Homework Assignment 1 - Revision history

Drorbn: Reverted edit of 62.231.243.138, changed back to last version by Wongpak

2007-06-16T06:16:04Z

Reverted edit of 62.231.243.138, changed back to last version by Wongpak

← Older revision		Revision as of 02:16, 16 June 2007
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	You seem unhappy, but I actually meant what I said. The equality <math>a^3=1</math> in a general field does not imply the equality <math>a\neq 1</math> --- why would it? After all, <math>a^2=1</math> does not imply <math>a\neq 1</math> either. Here are two examples for fields in which there is an <math>a\neq 1</math> for which <math>a^3=1</math>:		You seem unhappy, but I actually meant what I said. The equality <math>a^3=1</math> in a general field does not imply the equality <math>a\neq 1</math> --- why would it? After all, <math>a^2=1</math> does not imply <math>a\neq 1</math> either. Here are two examples for fields in which there is an <math>a\neq 1</math> for which <math>a^3=1</math>:
	# Our field and our <math>a</math>.		# Our field and our <math>a</math>.
	# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12 \frac{\sqrt{3}}{2}i</math>.		# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12+\frac{\sqrt{3}}{2}i</math>.
	--[[User:Drorbn\|Drorbn]] 17:38, 24 September 2006 (EDT)		--[[User:Drorbn\|Drorbn]] 17:38, 24 September 2006 (EDT)

2007-06-16T01:34:51Z

← Older revision		Revision as of 21:34, 15 June 2007
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	You seem unhappy, but I actually meant what I said. The equality <math>a^3=1</math> in a general field does not imply the equality <math>a\neq 1</math> --- why would it? After all, <math>a^2=1</math> does not imply <math>a\neq 1</math> either. Here are two examples for fields in which there is an <math>a\neq 1</math> for which <math>a^3=1</math>:		You seem unhappy, but I actually meant what I said. The equality <math>a^3=1</math> in a general field does not imply the equality <math>a\neq 1</math> --- why would it? After all, <math>a^2=1</math> does not imply <math>a\neq 1</math> either. Here are two examples for fields in which there is an <math>a\neq 1</math> for which <math>a^3=1</math>:
	# Our field and our <math>a</math>.		# Our field and our <math>a</math>.
	# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12+\frac{\sqrt{3}}{2}i</math>.		# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12 \frac{\sqrt{3}}{2}i</math>.
	--[[User:Drorbn\|Drorbn]] 17:38, 24 September 2006 (EDT)		--[[User:Drorbn\|Drorbn]] 17:38, 24 September 2006 (EDT)

2006-09-26T12:28:25Z

← Older revision		Revision as of 08:28, 26 September 2006
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	== Assigment 1 Solution ==		== Assigment 1 Solution ==

			I would appreciate if you may notify for any error. [[Media:Assignment 1 Ans.pdf\|Assignment 1 Solution]]--[[User:Wongpak\|Wongpak]] 08:28, 26 September 2006 (EDT)
	[[Media:Assignment 1 Ans.pdf]]

2006-09-26T12:24:48Z

Assigment 1 Solution

← Older revision		Revision as of 08:24, 26 September 2006
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	Actually I guessed it had something to do with the field. But this concept is still new to me, I just can't convice myself a is not 1 when aaa=1...But that example of complex numbers is indeed very convincing....thank you for your patience :)		Actually I guessed it had something to do with the field. But this concept is still new to me, I just can't convice myself a is not 1 when aaa=1...But that example of complex numbers is indeed very convincing....thank you for your patience :)

			== Assigment 1 Solution ==

			[[Media:Assignment 1 Ans.pdf]]

2006-09-26T02:27:49Z

← Older revision		Revision as of 22:27, 25 September 2006
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	# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12+\frac{\sqrt{3}}{2}i</math>.		# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12+\frac{\sqrt{3}}{2}i</math>.
	--[[User:Drorbn\|Drorbn]] 17:38, 24 September 2006 (EDT)		--[[User:Drorbn\|Drorbn]] 17:38, 24 September 2006 (EDT)

			Actually I guessed it had something to do with the field. But this concept is still new to me, I just can't convice myself a is not 1 when aaa=1...But that example of complex numbers is indeed very convincing....thank you for your patience :)

2006-09-24T21:38:48Z

← Older revision		Revision as of 17:38, 24 September 2006
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	# Our field and our <math>a</math>.		# Our field and our <math>a</math>.
	# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12+\frac{\sqrt{3}}{2}i</math>.		# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12+\frac{\sqrt{3}}{2}i</math>.
			--[[User:Drorbn\|Drorbn]] 17:38, 24 September 2006 (EDT)

2006-09-24T21:38:35Z

← Older revision		Revision as of 17:38, 24 September 2006
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	ok.....that's....very...convincing......I'll shut up...		ok.....that's....very...convincing......I'll shut up...

			You seem unhappy, but I actually meant what I said. The equality <math>a^3=1</math> in a general field does not imply the equality <math>a\neq 1</math> --- why would it? After all, <math>a^2=1</math> does not imply <math>a\neq 1</math> either. Here are two examples for fields in which there is an <math>a\neq 1</math> for which <math>a^3=1</math>:
			# Our field and our <math>a</math>.
			# The complex numbers <math>{\mathbb C}</math> and <math>a=-\frac12+\frac{\sqrt{3}}{2}i</math>.

2006-09-23T21:55:01Z

← Older revision		Revision as of 17:55, 23 September 2006
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	Well, OUR very own field has an element <math>a</math> for which <math>a^3=1</math> yet <math>a\neq 1</math>... --[[User:Drorbn\|Drorbn]] 17:08, 23 September 2006 (EDT)		Well, OUR very own field has an element <math>a</math> for which <math>a^3=1</math> yet <math>a\neq 1</math>... --[[User:Drorbn\|Drorbn]] 17:08, 23 September 2006 (EDT)

			ok.....that's....very...convincing......I'll shut up...

2006-09-23T21:08:16Z

← Older revision		Revision as of 17:08, 23 September 2006
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	er....since <math>aa^2=a^3=1</math>, or am I right about <math>aa^2=a^3</math>?....and what makes <math>a^3=1</math> except a=1?...sorry but please tell me where I got wrong.........		er....since <math>aa^2=a^3=1</math>, or am I right about <math>aa^2=a^3</math>?....and what makes <math>a^3=1</math> except a=1?...sorry but please tell me where I got wrong.........

			Well, OUR very own field has an element <math>a</math> for which <math>a^3=1</math> yet <math>a\neq 1</math>... --[[User:Drorbn\|Drorbn]] 17:08, 23 September 2006 (EDT)

2006-09-23T17:04:24Z

← Older revision		Revision as of 13:04, 23 September 2006
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	Repeat: I don't see why <math>a*a^2=1</math> implies <math>a=1</math>. --[[User:Drorbn\|Drorbn]] 03:24, 23 September 2006 (EDT)		Repeat: I don't see why <math>a*a^2=1</math> implies <math>a=1</math>. --[[User:Drorbn\|Drorbn]] 03:24, 23 September 2006 (EDT)

			er....since <math>aa^2=a^3=1</math>, or am I right about <math>aa^2=a^3</math>?....and what makes <math>a^3=1</math> except a=1?...sorry but please tell me where I got wrong.........