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02052013, 08:28 PM  #751 
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Joined: Feb 2010
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I see the Pope on fire
just went away, fuckin internet. oh, he's back, fuckin internet, 
02052013, 08:38 PM  #752 
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I'll bet the are a subset of this bad boy
You do remember your set theory, don't you??
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2008 WR250R  Tru Blu "Life's been good to me so far"  Joe Walsh 
02052013, 08:39 PM  #753  
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02052013, 08:42 PM  #754 
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Just in case you forgot...................
The history of set theory is rather different from the history of most other areas of mathematics. For most areas a long process can usually be traced in which ideas evolve until an ultimate flash of inspiration, often by a number of mathematicians almost simultaneously, produces a discovery of major importance. Set theory however is rather different. It is the creation of one person, Georg Cantor. Before we take up the main story of Cantor's development of the theory, we first examine some early contributions. The idea of infinity had been the subject of deep thought from the time of the Greeks. Zeno of Elea, in around 450 BC, with his problems on the infinite, made an early major contribution. By the Middle Ages discussion of the infinite had led to comparison of infinite sets. For example Albert of Saxony, in Questiones subtilissime in libros de celo et mundi, proves that a beam of infinite length has the same volume as 3space. He proves this by sawing the beam into imaginary pieces which he then assembles into successive concentric shells which fill space. Bolzano was a philosopher and mathematician of great depth of thought. In 1847 he considered sets with the following definition an embodiment of the idea or concept which we conceive when we regard the arrangement of its parts as a matter of indifference.Bolzano defended the concept of an infinite set. At this time many believed that infinite sets could not exist. Bolzano gave examples to show that, unlike for finite sets, the elements of an infinite set could be put in 11 correspondence with elements of one of its proper subsets. This idea eventually came to be used in the definition of a finite set. It was with Cantor's work however that set theory came to be put on a proper mathematical basis. Cantor's early work was in number theory and he published a number of articles on this topic between 1867 and 1871. These, although of high quality, give no indication that they were written by a man about to change the whole course of mathematics. An event of major importance occurred in 1872 when Cantor made a trip to Switzerland. There Cantor met Richard Dedekind and a friendship grew up that was to last for many years. Numerous letters between the two in the years 18731879 are preserved and although these discuss relatively little mathematics it is clear that Dedekind's deep abstract logical way of thinking was a major influence on Cantor as his ideas developed. Cantor moved from number theory to papers on trigonometric series. These papers contain Cantor's first ideas on set theory and also important results on irrational numbers. Dedekind was working independently on irrational numbers and Dedekind published Continuity and irrational numbers. In 1874 Cantor published an article in Crelle's Journal which marks the birth of set theory. A followup paper was submitted by Cantor to Crelle's Journal in 1878 but already set theory was becoming the centre of controversy. Kronecker, who was on the editorial staff of Crelle's Journal, was unhappy about the revolutionary new ideas contained in Cantor's paper. Cantor was tempted to withdraw the paper but Dedekind persuaded Cantor not to withdraw it and Weierstrass supported publication. The paper was published but Cantor never submitted any further work to Crelle's Journal. In his 1874 paper Cantor considers at least two different kinds of infinity. Before this orders of infinity did not exist but all infinite collections were considered 'the same size'. However Cantor examines the set of algebraic real numbers, that is the set of all real roots of equations of the form a_{n} x^{n} + a_{n1} x^{n1} + a_{n2} x^{n2} + . . . + a_{1} x + a_{0} = 0,
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2008 WR250R  Tru Blu "Life's been good to me so far"  Joe Walsh 
02052013, 08:42 PM  #755  
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Quote:
where do you think I hang out when im not posting..Ive seen your trailer thread
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On the plains of hesitation lie the blackened bones of countless millions who at the dawn of victory lay down to rest, and in resting died. Go forth and be a force of the awesome! 

02052013, 08:46 PM  #756  
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Quote:
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On the plains of hesitation lie the blackened bones of countless millions who at the dawn of victory lay down to rest, and in resting died. Go forth and be a force of the awesome! 

02052013, 08:48 PM  #757 
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Location: CT
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Time to go harass clowns and or people in Honda Fits.

02052013, 08:48 PM  #758 
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In addition to the test......................................
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2008 WR250R  Tru Blu "Life's been good to me so far"  Joe Walsh 
02052013, 08:50 PM  #759 
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"Heavy? Heavy? Marty, is there something wrong with the gravity in 1985?"
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2008 WR250R  Tru Blu "Life's been good to me so far"  Joe Walsh 
02052013, 08:53 PM  #760 
Crazy Idiot
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On the plains of hesitation lie the blackened bones of countless millions who at the dawn of victory lay down to rest, and in resting died. Go forth and be a force of the awesome! 
02052013, 08:54 PM  #761 
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Don't be messin' wit dis CLOWN, dawg. He gonna open up a can of whomp ass on yo sorry butt.
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2008 WR250R  Tru Blu "Life's been good to me so far"  Joe Walsh 
02052013, 08:58 PM  #762  
found second gear
Joined: Sep 2009
Location: nw connecticut
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Quote:
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I ride to get away from society not to go towards it Life's too short to hang out with people that piss you off 

02052013, 09:13 PM  #763 
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Pimp master Leif does not like them puppies
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On the plains of hesitation lie the blackened bones of countless millions who at the dawn of victory lay down to rest, and in resting died. Go forth and be a force of the awesome! 
02052013, 09:34 PM  #764 
Crazy Idiot
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Location: Romaniacs 2019
Oddometer: 24,412

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On the plains of hesitation lie the blackened bones of countless millions who at the dawn of victory lay down to rest, and in resting died. Go forth and be a force of the awesome! 
02062013, 03:36 AM  #765 
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Woo Woo  Another snow day. No school for BP.
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2008 WR250R  Tru Blu "Life's been good to me so far"  Joe Walsh 
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