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I gave an answer to your RD/math question there. The idea is salvageable - if all possible absolute values of an algebraic number are 1, then it must be a root of unity. To be more concrete, if u is a complex number which is an algebraic integer (its irreducible polynomial f(x) over Z is monic), and if all the complex roots of f have absolute value 1, then u must be a root of unity.
The final /constant coefficient of f is just the product of all the roots of f, so if all of these have AV 1, then the final coefficient is an integer with AV 1, i.e. 1 or -1. Because the irreducible poly of (1/u) is the same as f, except for the coefficients being reversed, this implies that the irr poly for (1/u) is monic, and that (1/u) is an algebraic integer too, and thus a unit in any ring of integers of a number field, (which is equivalent to saying that all the p-adic absolute values of u are 1). Then the argument I gave at the ref desk shows that u must be a root of unity. John Z ( talk) 20:59, 2 May 2009 (UTC)
COVIZAPIBETEFOKY, Would you care to activate your email ie "email this user" feature? Coviza2 ( talk) 16:06, 25 May 2009 (UTC)
Just to let you know that I've made this edit. Your contributions at the math desk seem well thought out and helpful. Thank you! hydnjo ( talk) 21:45, 17 June 2009 (UTC)
Hi COVIZA, I've started a discussion on the .9... article here. You should probably participate in the discussion. Best, ceran thor 19:17, 26 October 2009 (UTC)
Click here for context. -- COVIZAPIBETEFOKY ( talk) 17:52, 7 January 2011 (UTC)
look up percentages for basic literacy, and tell me based on that how much more qualified, statistically, white people are for being president than black people. 87.91.6.33 ( talk) 11:40, 7 January 2011 (UTC)
Don't worry about it, Quest09. I'm kind of enjoying this, actually. You don't see a case of such deliberately self-imposed cognitive dissonance very often. -- COVIZAPIBETEFOKY ( talk) 14:26, 12 January 2011 (UTC)
Haha what in the world does your username mean?? JamesMazur22 ( talk) 18:38, 25 June 2011 (UTC)
Just a suggestion to remove your comment, firstly since calling someone a moron is a straightforward violation of no personal attacks, and secondly because replying to this guy (who it's pretty clear is also the person who doesn't believe in mathematics) looks like it's almost certainly feeding the troll. Confusing Manifestation( Say hi!) 23:27, 4 July 2011 (UTC)
Hello, and welcome to Wikipedia. Although everyone is welcome to contribute to Wikipedia, at least one of your recent edits, such as the one you made to Talk:0.999..., did not appear to be constructive and has been reverted or removed. Please use the sandbox for any test edits you would like to make, and read the welcome page to learn more about contributing constructively to this encyclopedia. Thank you. JohnBlackburne words deeds 14:39, 1 January 2012 (UTC)
Welcome, and thank you for your attempt to lighten up Wikipedia. However, this is an encyclopedia and the articles are intended to be serious, so please don't make joke edits, as you did to Wikipedia:Reference desk/Mathematics. Readers looking for accurate information will not find them amusing. If you'd like to experiment with editing, try the sandbox, where you can write practically anything you want. JohnBlackburne words deeds 23:51, 8 March 2012 (UTC)
Can you please explain why you left a comment using someone else's signature, and then reverted SineBot to maintain what appears to be a signature forgery? Singularity42 ( talk) 14:24, 9 September 2012 (UTC)
Hello. There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. The thread is COVIZAPIBETEFOKY (talk · contribs): signature forgery and personal attacks. Thank you. Singularity42 ( talk) 15:37, 9 September 2012 (UTC)
COVIZAPIBETEFOKY, it's really not ok do that. I see you around the math ref desk sometimes and you post good stuff there. I haven't looked at Algr's posts so I don't have any opinion of them, but faking other users' signatures and calling people retards is unsubtle enough that it's going to swamp out any deficiencies in Algr's posts, and attract outside intervention and probably get you blocked. Can you please agree to cut it out? This is the encyclopedia anyone can edit, and of course articles like 0.999... are going to attract contributors with strong opinions and weak mathematical understanding ( WP:RANDY). If you have trouble dealing civilly with such editors, it's best to work on articles where they don't congregate. 67.119.15.30 ( talk) 16:41, 9 September 2012 (UTC)
{{
unblock|reason=Your reason here ~~~~}}
, but you should read the
guide to appealing blocks first. --
Boing! said Zebedee (
talk)
18:01, 9 September 2012 (UTC)
|
I gave an answer to your RD/math question there. The idea is salvageable - if all possible absolute values of an algebraic number are 1, then it must be a root of unity. To be more concrete, if u is a complex number which is an algebraic integer (its irreducible polynomial f(x) over Z is monic), and if all the complex roots of f have absolute value 1, then u must be a root of unity.
The final /constant coefficient of f is just the product of all the roots of f, so if all of these have AV 1, then the final coefficient is an integer with AV 1, i.e. 1 or -1. Because the irreducible poly of (1/u) is the same as f, except for the coefficients being reversed, this implies that the irr poly for (1/u) is monic, and that (1/u) is an algebraic integer too, and thus a unit in any ring of integers of a number field, (which is equivalent to saying that all the p-adic absolute values of u are 1). Then the argument I gave at the ref desk shows that u must be a root of unity. John Z ( talk) 20:59, 2 May 2009 (UTC)
COVIZAPIBETEFOKY, Would you care to activate your email ie "email this user" feature? Coviza2 ( talk) 16:06, 25 May 2009 (UTC)
Just to let you know that I've made this edit. Your contributions at the math desk seem well thought out and helpful. Thank you! hydnjo ( talk) 21:45, 17 June 2009 (UTC)
Hi COVIZA, I've started a discussion on the .9... article here. You should probably participate in the discussion. Best, ceran thor 19:17, 26 October 2009 (UTC)
Click here for context. -- COVIZAPIBETEFOKY ( talk) 17:52, 7 January 2011 (UTC)
look up percentages for basic literacy, and tell me based on that how much more qualified, statistically, white people are for being president than black people. 87.91.6.33 ( talk) 11:40, 7 January 2011 (UTC)
Don't worry about it, Quest09. I'm kind of enjoying this, actually. You don't see a case of such deliberately self-imposed cognitive dissonance very often. -- COVIZAPIBETEFOKY ( talk) 14:26, 12 January 2011 (UTC)
Haha what in the world does your username mean?? JamesMazur22 ( talk) 18:38, 25 June 2011 (UTC)
Just a suggestion to remove your comment, firstly since calling someone a moron is a straightforward violation of no personal attacks, and secondly because replying to this guy (who it's pretty clear is also the person who doesn't believe in mathematics) looks like it's almost certainly feeding the troll. Confusing Manifestation( Say hi!) 23:27, 4 July 2011 (UTC)
Hello, and welcome to Wikipedia. Although everyone is welcome to contribute to Wikipedia, at least one of your recent edits, such as the one you made to Talk:0.999..., did not appear to be constructive and has been reverted or removed. Please use the sandbox for any test edits you would like to make, and read the welcome page to learn more about contributing constructively to this encyclopedia. Thank you. JohnBlackburne words deeds 14:39, 1 January 2012 (UTC)
Welcome, and thank you for your attempt to lighten up Wikipedia. However, this is an encyclopedia and the articles are intended to be serious, so please don't make joke edits, as you did to Wikipedia:Reference desk/Mathematics. Readers looking for accurate information will not find them amusing. If you'd like to experiment with editing, try the sandbox, where you can write practically anything you want. JohnBlackburne words deeds 23:51, 8 March 2012 (UTC)
Can you please explain why you left a comment using someone else's signature, and then reverted SineBot to maintain what appears to be a signature forgery? Singularity42 ( talk) 14:24, 9 September 2012 (UTC)
Hello. There is currently a discussion at Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. The thread is COVIZAPIBETEFOKY (talk · contribs): signature forgery and personal attacks. Thank you. Singularity42 ( talk) 15:37, 9 September 2012 (UTC)
COVIZAPIBETEFOKY, it's really not ok do that. I see you around the math ref desk sometimes and you post good stuff there. I haven't looked at Algr's posts so I don't have any opinion of them, but faking other users' signatures and calling people retards is unsubtle enough that it's going to swamp out any deficiencies in Algr's posts, and attract outside intervention and probably get you blocked. Can you please agree to cut it out? This is the encyclopedia anyone can edit, and of course articles like 0.999... are going to attract contributors with strong opinions and weak mathematical understanding ( WP:RANDY). If you have trouble dealing civilly with such editors, it's best to work on articles where they don't congregate. 67.119.15.30 ( talk) 16:41, 9 September 2012 (UTC)
{{
unblock|reason=Your reason here ~~~~}}
, but you should read the
guide to appealing blocks first. --
Boing! said Zebedee (
talk)
18:01, 9 September 2012 (UTC)