Senthil Kumaran (Posts about maths)http://www.xtoinfinity.com/enMon, 21 Jun 2021 05:13:21 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rssWhat is the proof that total number of subsets of a set is 2^n?http://www.xtoinfinity.com/posts/what-is-the-proof-that-total-number-of-subsets-of-a-set-is-2n.htmlSenthil Kumaran<div><p>I have known "by heart" that total number of the subsets of a set of n number is <span class="math">\(2^n\)</span>
I was struggling to find an intuitive explanation, and two answers helped me to understand it.</p>
<blockquote>
For each element, you have two choices: either you put it in your subset, or you don't; and these choices are all
independent.</blockquote>
<p>Citation:</p>
<p>Bruno Joyal (<a class="reference external" href="https://math.stackexchange.com/users/12507/bruno-joyal">https://math.stackexchange.com/users/12507/bruno-joyal</a>), What is the proof that the total number of
subsets of a set is $2^n$?, URL (version: 2013-10-31): <a class="reference external" href="https://math.stackexchange.com/q/546417">https://math.stackexchange.com/q/546417</a></p>
<p>Another was this table that represented the sets as binary, to denote 0 as an absence of the element and 1 as presence
of the element.</p>
<img alt="https://dl.dropbox.com/s/0smcrv98o8igrhh/power_set.jpg" src="https://dl.dropbox.com/s/0smcrv98o8igrhh/power_set.jpg">
<p>That can help us understand that the total number of subsets of set of n is <span class="math">\(2^n\)</span></p></div>mathshttp://www.xtoinfinity.com/posts/what-is-the-proof-that-total-number-of-subsets-of-a-set-is-2n.htmlTue, 29 Jan 2019 13:18:44 GMTRadians and Roger Coatshttp://www.xtoinfinity.com/posts/2018/02/17/radians-and-roger-coats.htmlSenthil Kumaran<div><p>When trying to understand the concept of <a class="reference external" href="https://en.wikipedia.org/wiki/Radian#History">radians</a>, I came across the inventor of the concept <a class="reference external" href="https://en.wikipedia.org/wiki/Roger_Cotes">Roger Coats</a>
His name is not familiar to many. I understood, he is known for working closely with Isaac Newton by proofreading the
second edition of his famous book, the Principia, before publication.</p>
<p>Cotes died from a violent fever in Cambridge in 1716 at the early age of 33. Isaac Newton remarked, "If he had lived we would have known something."</p></div>mathshttp://www.xtoinfinity.com/posts/2018/02/17/radians-and-roger-coats.htmlSat, 17 Feb 2018 21:23:54 GMT