tag:blogger.com,1999:blog-3711403820684618858.post1557227512488324798..comments2016-11-03T09:58:44.102-07:00Comments on Juridical Coherence: 19.2. Infinitesimals: Another argument against actual infinite setsStephen R. Diamondhttp://www.blogger.com/profile/07165258952900481659noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-3711403820684618858.post-37349011121447700322016-11-03T04:39:36.728-07:002016-11-03T04:39:36.728-07:00Cantor's theory fails because there is no comp...Cantor's theory fails because there is no completed infinity.<br /><br />According to set theory the figure<br />1<br />2, 1<br />3, 2, 1<br />...<br />contains an infinite number of elements, namely all natural numbers.<br /><br />No row of the figure contains an infinite number of elements.<br /><br />According to mathematics, the figure is an inclusion-monotonic sequence of finite rows. That means: Every union of finite rows is contained in one of the unioned rows. (The principle of construction shows, that this property is independent of the number of finite rows. Otherwise there would be a first finite row that does not contain all elements of its predecessors.) If the contents of the figure is a fixed quantity, then this fixed quantity is in one of its rows. Contradiction. Therefore the idea of the natural numbers being a fixed quantity can be excluded.<br /><br />Regards, WMWMhttp://www.blogger.com/profile/15911521190071762395noreply@blogger.com