tag:blogger.com,1999:blog-1293406215612885491.post9036577305996765280..comments2023-03-21T09:40:03.723-07:00Comments on Piles of Philosophy: Reason vs intuitionWaynehttp://www.blogger.com/profile/08627147979307495870noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-1293406215612885491.post-39645155764778177802010-03-08T13:26:56.917-08:002010-03-08T13:26:56.917-08:00no it wouldn't extend to the arbitrarily large...no it wouldn't extend to the arbitrarily large. It only works with infinite sequences. Practically they may be identical, but mathematically they're not.Waynehttps://www.blogger.com/profile/08627147979307495870noreply@blogger.comtag:blogger.com,1999:blog-1293406215612885491.post-72897951695600738352010-03-08T09:47:04.134-08:002010-03-08T09:47:04.134-08:00Oh well. I have to concede the point. Reading furt...Oh well. I have to concede the point. Reading further into the definition, .33_ is 1/3, just as .5 is 1/2. Fair enough. .99_ is 1. I'm wondering if one could extend the logic to an absurdly large number of zeros followed by a 1, ex: 1.000000000000000000000000000000000001 = 1. For all intents, they're practically the same, right? If you round from the Tera, Yotta or "Hella" scale, it is 1. Or even more interestingly, 0 = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001. Same number? Almost the same logic, but somehow not exactly the same. A = ~exactly A. The math is saying that though we're using different symbols to represent them, the numbers are in fact identical, by definition. But that my follow on, which would seem somewhat logical, doesn't actually fly, because there is a difference between a decimal which actually repeats to infinity and one that just comes really close.GDBnoreply@blogger.comtag:blogger.com,1999:blog-1293406215612885491.post-7104041379543356522010-03-06T20:33:39.352-08:002010-03-06T20:33:39.352-08:00I hope I've never given the impression that I&...I hope I've never given the impression that I'm rejecting your points because they sound silly. I do notice it though, and I find that lack of real critical thinking annoying.<br /><br />Although I would like to say that, after given a lot of thought, I could maybe point out a few arguments against two of the thought experiments you've presented us with, as well as the achilles/tortoise thing. (Not really arguments against them, but just things that point to how cheap they are). I just have a hard time articulating my thoughts on the spot, which is why I don't talk all the time in class.Kylehttps://www.blogger.com/profile/16211037960656808895noreply@blogger.comtag:blogger.com,1999:blog-1293406215612885491.post-49016390850975633052010-03-05T12:38:27.440-08:002010-03-05T12:38:27.440-08:00Hmmm... maybe I failed to point out that the elips...Hmmm... maybe I failed to point out that the elipsis at the end of .333333... refers to an infinite string of 3s.Waynehttps://www.blogger.com/profile/08627147979307495870noreply@blogger.comtag:blogger.com,1999:blog-1293406215612885491.post-12258129012402638842010-03-05T12:36:49.469-08:002010-03-05T12:36:49.469-08:00Nope its not a shorthand illusion. They really ar...Nope its not a shorthand illusion. They really are equal. Its not even all that controversial in the math world.<br /><br />http://en.wikipedia.org/wiki/0.999...<br />http://mathforum.org/dr.math/faq/faq.0.9999.html<br /><br />I've even seen it in textbooks.Waynehttps://www.blogger.com/profile/08627147979307495870noreply@blogger.comtag:blogger.com,1999:blog-1293406215612885491.post-3517127999175343032010-03-05T10:28:33.325-08:002010-03-05T10:28:33.325-08:00While I agree that often our intutions are wrong w...While I agree that often our intutions are wrong when faced with either reason or experience, I don't think your math is right. <br />I don't agree that 1/3 = .33333333333 (etc).<br />They are very close to each other, and in math, we typically use them interchangeably as a shortcut, but they are not the exact same number any more than .999999999999999999 is the exact same number as 1. It is mathmatically and by definition true that 1/3+2/3=1 and .333+.666=.999, but 1/3 is not equal to .333333333333333333333, its just a shortcut.GDBnoreply@blogger.com