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January 27th, 2014, 11:04 PM  #1 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  irrational numbers
prove: are all irrational numbers 
January 28th, 2014, 02:07 AM  #2  
Senior Member Joined: May 2013 From: EspaÃ±a Posts: 151 Thanks: 4  Re: irrational numbers Quote:
I will realize the cosine: (*) 1º) If "q" It is divisible only once by "2", then: Absurdity: 2º) The rest of the show, leave it to someone else. Regards.  
January 28th, 2014, 04:50 AM  #3 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: irrational numbers
In general, it is provably true that and are both rational only for finitely many values of , i.e, one of 0, 1/2, or 1 (+ or ).

February 12th, 2014, 03:26 PM  #4  
Senior Member Joined: May 2013 From: EspaÃ±a Posts: 151 Thanks: 4  Re: irrational numbers
[quote=mente oscura] Quote:
I will realize the cosine: [/quote:337yooi9] Hello. I'm sorry. I had a mistake at the beginning. Suppose, : , Absurdity: If we had started by: (*) 1º) If "q" It is divisible only once by "2", then: Absurdity: 2º) Regards.  
February 12th, 2014, 04:55 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: irrational numbers The equation immediately above, by the rational root theorem, has no rational roots, hence sin(10) is irrational. A similar proof can be constructed for cos(10). 

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