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01242009, 01:03 PM  #1  
 
Class 3R Laser Join Date: Oct 2008 Location: So. Cal.
Posts: 1,059
Rep Power: 124 
My calc 3 professor showed us this the other day and I thought I would try to explain it to you. When a number is irrational it means that it cannot be represented as a fraction of two integers nor can it be represented as a terminating or repeating decimal number. Pi is irrational. It is a decimal number that will go on forever and is non repeating. So to prove that [ch8730]2 is irrational you can justify an incorrect condition and then contradict it. So say [ch8730]2 is rational. Then [ch8730]2=p/q * The fraction p/q is irreducible. (This is important you will see why at the end). p=[ch8730]2q p[sup]2[/sup]=2q[sup]2[/sup] * 2q[sup]2[/sup] must be an even number. Therefor p[sup]2[/sup] must be even and p must also be even. Squaring an odd number yields a odd number, it's the same with even numbers too. So since p is even we can say p=2k * k must be an integer. By substituting we have (2k)[sup]2[/sup]=2q[sup]2[/sup] 4k[sup]2[/sup]=2q[sup]2[/sup] 2k[sup]2[/sup]=q[sup]2[/sup] * By the logic explained above we can conclude that q must also be even. so [ch8730]2=p/q but if p and q are even then the fraction p/q is reducible by at least 2. By contradicting the initial condition that p and q are not coprime [ch8730]2 must not be rational because the math showing it could be represented as a irreducible fraction contradicted itself. Isn't math fun! ;D Tony
__________________ 300mW 808nm IR Burner 250mW 660nm LOC Ehgemus Torch 5mW 635nm ZBolt Pointer 160mW 532nm CNI PGLIIIA 10mW 473nm B&W Tek BWB10OEM 300mW 445nm Ehgemus CR123 Build 260mW 405nm 6x Ehgemus Torch 20mW Magenta 405nm + 660nm PS3 Hybird Aixiz Pointer Know Your Wavelength  
01242009, 01:56 PM  #2  
 
Class 3R Laser Join Date: Jan 2008
Posts: 1,864
Rep Power: 132 
__________________ Used to have 26 rep points I am leet  
01242009, 04:33 PM  #3  
 
Cereal Eater  Quote:
I've seen this explanation lots of times but I had never dedicated time to really read it until now.  
01242009, 05:53 PM  #4  
 
Class 2 Laser Join Date: Oct 2008
Posts: 337
Rep Power: 14 
This is called reductio ad absurdum if I remember correctly. It's a clever way to prove things. What's with all the math threads lately?  
01252009, 02:20 AM  #5  
 
Class 3R Laser Join Date: Aug 2008 Location: Washington
Posts: 1,368
Rep Power: 47 
I think there should be an official math thread. But I'm not going to make it, because my threads always die in a day or two. Mark  
01252009, 02:22 AM  #6  
 
Banned Join Date: Mar 2008 Location: Austin TX
Posts: 1,341
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NO, WE NEED A MATH SECTION! as well as a sections for flaming  
01252009, 02:40 AM  #7  
 
Class 2 Laser 
um.... :? u lost me after the 1st number... lol
__________________ not fast enough..  
01252009, 02:42 AM  #8  
 
Cereal Eater  Quote:
No flame section, yes to the math thread. Will [s]spam[/s] create it right away!  
01252009, 07:02 AM  #9  
 
Class 3R Laser Join Date: Oct 2008 Location: So. Cal.
Posts: 1,059
Rep Power: 124  Quote:
A fraction of an even number over an even number is reducible. 2/4 is 1/2. A fraction that is irreducible must have an odd numerator or denominator. So setting by [ch8730]2=p/q and saying that p/q is irreducible then through mathematical operations we prove that p and q are even p/q is reducible. Since the logic contradicts itself we can conclude that [ch8730]2 cannot be set equal to a ratio of two integers. I love math because it is derived from logic and reasoning. You can write a paper or story that some may not like. I hate English and history! Who the hell cares what happened yesterday! This country does not learn from its mistakes. So don't pull that card. But math is either right or wrong (period!!!). Does anyone get the proof? I cant be the only math person on this forum. Tony
__________________ 300mW 808nm IR Burner 250mW 660nm LOC Ehgemus Torch 5mW 635nm ZBolt Pointer 160mW 532nm CNI PGLIIIA 10mW 473nm B&W Tek BWB10OEM 300mW 445nm Ehgemus CR123 Build 260mW 405nm 6x Ehgemus Torch 20mW Magenta 405nm + 660nm PS3 Hybird Aixiz Pointer Know Your Wavelength  
01252009, 04:13 PM  #10  
 
Class 3R Laser Join Date: Apr 2008 Location: South Florida
Posts: 1,543
Rep Power: 135 
I got lost at Quote:
__________________ Current Lasers: 8??nm: 1050mA DIY Micro Sized 658nm: 2mW keychain pointer  DIY 80mA/350mA switchable in Altoids tin  300mA DIY Micro Sized 632.8nm: 10mW Hughes HeNe  15mW Melles Griot HeNe  1mW Melles Griot bare tube 612nm: 5mW Meredith Instruments HeNe 594.1nm: 4mW Meredith Instruments HeNe 543nm: 2mW Melles Griot HeNe  <1mW Multimode 6" HeNe (He's cute!) 532nm: 5mW LyraG5  70mW DIY by Wannaburn 473nm: 5mW Lab Style 445nm: DIY 650mA in Sonar II Host 405nm: DIY LG 10X at 330mA with Ehgemus host and Microboost  CNI GLP405 70mW  
01252009, 05:31 PM  #11  
 
Cereal Eater  Quote:
A fraction of an even number over an even number is reducible. 2/4 is 1/2. A fraction that is irreducible must have an odd numerator or denominator. So setting by [ch8730]2=p/q and saying that p/q is irreducible then through mathematical operations we prove that p and q are even p/q is reducible. Since the logic contradicts itself we can conclude that [ch8730]2 cannot be set equal to a ratio of two integers. I love math because it is derived from logic and reasoning. You can write a paper or story that some may not like. I hate English and history! Who the hell cares what happened yesterday! This country does not learn from its mistakes. So don't pull that card. But math is either right or wrong (period!!!). Does anyone get the proof? I cant be the only math person on this forum. Tony[/quote] OH MY CHUCK I've just realised what I wrote, LOL. I completely get it now, thanks! :P  
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