tag:blogger.com,1999:blog-17504635.post114738929014866483..comments2023-11-03T03:25:58.422-04:00Comments on MathCog Idiocy: More orderAnonymoushttp://www.blogger.com/profile/14350832388608921347noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-17504635.post-1147475035609613232006-05-12T19:03:00.000-04:002006-05-12T19:03:00.000-04:00Teresa -The statement "every non-empty set of nega...Teresa -<BR/><BR/>The statement "every non-empty set of negative integers has a largest element" is certainly a true statement. However within the grander scheme of number theory, it doesn't necessarily add anything, but instead sets up a situation where the concept of order becomes indidually defined for each non-empty set. There's a loss of generality. Not a good thing.<BR/><BR/>There's also the fact that the well-ordered property is applied in a more general sense where any non-empty set with a least element is considered well-ordered.Anonymoushttps://www.blogger.com/profile/14350832388608921347noreply@blogger.comtag:blogger.com,1999:blog-17504635.post-1147474640030118342006-05-12T18:57:00.000-04:002006-05-12T18:57:00.000-04:00"low fat side of the menu" *snork*"low fat side of the menu" *snork*Anonymoushttps://www.blogger.com/profile/14350832388608921347noreply@blogger.comtag:blogger.com,1999:blog-17504635.post-1147455230567469302006-05-12T13:33:00.000-04:002006-05-12T13:33:00.000-04:00I don't suppose it could be turned around for nega...I don't suppose it could be turned around for negative numbers. <BR/><BR/>Every non-empty set of negative integers has a largest element. <BR/><BR/>Yeah my brain is not not not working today.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17504635.post-1147430733770294222006-05-12T06:45:00.000-04:002006-05-12T06:45:00.000-04:00And I thougth Well ordering meant you stuck to the...And I thougth Well ordering meant you stuck to the low fat side of the menu.Anonymousnoreply@blogger.com