{"id":305,"date":"2008-12-20T07:09:04","date_gmt":"2008-12-20T07:09:04","guid":{"rendered":"https:\/\/amperzen.com\/blog\/?p=305"},"modified":"2008-12-20T18:44:11","modified_gmt":"2008-12-20T18:44:11","slug":"mathematical-things-i-think-about-when-its-too-late-at-night","status":"publish","type":"post","link":"https:\/\/amperzen.com\/blog\/mathematical-things-i-think-about-when-its-too-late-at-night\/","title":{"rendered":"Mathematical things I think about when it’s too late at night"},"content":{"rendered":"

\"Hyperion<\/p>\n

While I’m sure this comes as no big question to professional mathematicians, I’ve never come to an understanding of the nature of infinity. The question that came up this evening while sitting at a traffic light was: if the set of integer numbers is infinite, and the set of real numbers is infinite, and integers are a subset of real numbers, then isn’t one infinity larger than the other? Furthermore, if you subtract the integers from the reals, you still have an infinite set left over. Now take the numbers X\/10, where X is an integer. There’s an infinite number of them too. And X\/100, X\/1000, on and on with increasing powers of 10 in the denominator. Obviously, there’s an infinite number of them as well. Plus X\/2, X\/20, X\/200, X\/3, X\/30, X\/300, etc etc etc. No matter how many infinite sets you take out, there’s still an infinite number left. So doesn’t that make the infinitely large set of real numbers infinitely larger than the infinite set of integers? <\/p>\n

So, there’s no solution here, no grand philosophy, no rant. Just the simple acknowledgment that I really don’t understand the concept of infinity, and I wonder if anyone really does?<\/p>\n","protected":false},"excerpt":{"rendered":"

While I’m sure this comes as no big question to professional mathematicians, I’ve never come to an understanding of the nature of infinity. The question that came up this evening while sitting at a traffic light was: if the set of integer numbers is infinite, and the set of real numbers is infinite, and integers […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16,25],"tags":[],"class_list":["post-305","post","type-post","status-publish","format-standard","hentry","category-hyperion","category-science"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t