tag:blogger.com,1999:blog-913609798232369293.post7349340897785783533..comments2019-09-02T12:30:06.801-07:00Comments on Europrogocontestovision: Book of SandAdam Roberts Projecthttp://www.blogger.com/profile/10001572970456425902noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-913609798232369293.post-27894555614225953002011-12-18T21:26:14.222-08:002011-12-18T21:26:14.222-08:00In the low cost mobile genre, the offerings from K...In the low cost mobile genre, the offerings from Karbonn are certainly the ripple creator among the users. Low cost with feature richness is what Karbonn is known for, and a perfect companion for your connection that RightShopping.in places. Check www.rightshopping.in/g/itb.asp?C=Karbonn-Mobile-Phones&b=Karbonn&cid=1 now.ANUPAMAhttps://www.blogger.com/profile/12347945861518973268noreply@blogger.comtag:blogger.com,1999:blog-913609798232369293.post-12560662888199778402011-12-16T15:23:41.171-08:002011-12-16T15:23:41.171-08:00You've hit upon one of the foundational diffic...You've hit upon one of the foundational difficulties in set theory, which is solved by the concept of <b>measure</b>.<br /><br />Sadly, the <a href="http://en.wikipedia.org/wiki/Measure_(mathematics)" rel="nofollow">Wikipedia article</a> is a bit high-level, so I'll sketch the background for you.<br /><br />One of the breakthroughs in the analysis of real numbers is the idea that you can think of a numerical interval (like the interval between 0 to 1) as a <i>set</i> consisting of the numbers in that interval, instead of (as before) some kind of geometrical object like a line segment.<br /><br />You can do lots of things with set-theoretic approach, but there's a stumbling block: you need to be able to reconstruct the notion of the <i>length</i> of an interval, which was straightforward in the geometric framework, but not so much in the set-theoretic framework, because an interval is an infinite set, and for infinite sets the notion of <i>size</i> is tricky, as witnessed by the <a href="http://en.wikipedia.org/wiki/Paradoxes_of_set_theory" rel="nofollow">paradoxes of set theory</a> such as <a href="http://en.wikipedia.org/wiki/Galileo%27s_paradox" rel="nofollow">Galileo's paradox of square numbers</a>, or <a href="http://en.wikipedia.org/wiki/Aristotle's_wheel_paradox" rel="nofollow">Aristotle's paradox of the wheel</a>.<br /><br />"Measures" are ways of assigning "sizes" to sets of real numbers that act like lengths for intervals, but extend to much wider ranges of sets. There are lots of different kinds of measure: <a href="http://en.wikipedia.org/wiki/Lebesgue_measure" rel="nofollow">Lebesgue measure</a> is one of the simplest (and historically one of the earliest).<br /><br />Measure solves your Book of Sand conundrum: your gold-painted subset of the book may have an infinite number of pages, but it only has half the measure of the whole book.Gareth Reeshttps://www.blogger.com/profile/15405124248006286547noreply@blogger.comtag:blogger.com,1999:blog-913609798232369293.post-81847291071345370382011-12-14T05:18:28.545-08:002011-12-14T05:18:28.545-08:00An inversion upon Zeno's paradox of Achilles a...An inversion upon Zeno's paradox of Achilles and the Tortoise … perhaps one could be embedded within the other for even more dizzying fun?Mahendra Singhhttps://www.blogger.com/profile/15308770582240496910noreply@blogger.com