tag:blogger.com,1999:blog-4290163255778893789.post1599224881230176708..comments2024-03-16T05:19:07.061-04:00Comments on Retirement Blues: What the Hell? Friday -- On the Primacy of the Number 1Jazzbumpahttp://www.blogger.com/profile/07337490817307473659noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-4290163255778893789.post-24180391937329394072010-07-23T23:46:55.095-04:002010-07-23T23:46:55.095-04:00I had no time to dig deeper today, and won't t...I had no time to dig deeper today, and won't tomorrow either.<br /><br />I do want to get to the bottom of this.<br /><br />I'll check the wiki link when I have more time.<br /><br />JzBJazzbumpahttps://www.blogger.com/profile/07337490817307473659noreply@blogger.comtag:blogger.com,1999:blog-4290163255778893789.post-88671923215853453532010-07-23T11:55:40.348-04:002010-07-23T11:55:40.348-04:00Again, I think it's done for...simplicity'...Again, I think it's done for...simplicity's sake--if the eggheads did allow 1 as prime then....any number could be factored in an infinite number of ways, via 1 and exponent: 5 = 5 x 1^to the 10th, and 5 = 5 x 1^ to the millionth. Messy bookkeeping. <br /><br />The Fundamental Theorem-- “each number has a unique factorization into primes"-- actually depends on one not being prime (see the wiki on primality).<br /><br />Erastothenes's ancient algorithm left one out. <br /><br />But analysis, schnalysis. Blogland wants....lifestyles of Rachel Maddow & friends, jzbJhttps://www.blogger.com/profile/11567400697675996283noreply@blogger.comtag:blogger.com,1999:blog-4290163255778893789.post-73454881532083664712010-07-23T11:18:59.748-04:002010-07-23T11:18:59.748-04:00Yet one and itself aren't two.
That is why i ...<i>Yet one and itself aren't two.</i><br /><br />That is why i call this a degenerate case. Both conditions: itself and one collapse to a single condition. This happens with electron energy levels in molecules, as confirmed by spectroscopy. I really don't see this a problem.<br /><br />The definition strikes me as being arbitrary, if not downright capricious. And the fundamental theorem fails if 1 is not a prime.<br /><br />When it's me against the entire edifice of mathematics, it's hard even for me to believe I'm right. But I can't find a valid argument to convince that I'm wrong.<br /><br />"It is because we say it is" is totally lame, and no science should work that way. I want something grounded in mathematical logic.<br /><br />Cheers!<br />JzBJazzbumpahttps://www.blogger.com/profile/07337490817307473659noreply@blogger.comtag:blogger.com,1999:blog-4290163255778893789.post-55774805309952119652010-07-23T10:44:10.540-04:002010-07-23T10:44:10.540-04:00A prime requires two divisors, One and itself. Yet...A prime requires two divisors, One and itself. Yet one and itself aren't two. Why is that the rule? Because. Sort of like asking, why do knights move the way they do in chess? 'Cuz that's how the game's played, for centuries (that doesn't mean that the chess rules...or natural numbers were written in stone...an abacus shows the origins of mathematics as well as greek philosophers do, ie bean counting) . Everything works out that way for the numbers' game. Holy Sieve of Erastothenes batman. <br /><br />You'd be surprised at how many academic mathematicians and logicians still believe numbers float in some platonic abode--like next to Truth, Justice and Euclidian axioms.Jhttps://www.blogger.com/profile/11567400697675996283noreply@blogger.com