<story><title>Cryptic genetic variation in software: hunting a buffered 41-year-old bug</title><url>https://cryptogenomicon.wordpress.com/2014/10/13/cryptic-genetic-variation-in-software-hunting-a-buffered-41-year-old-bug/</url></story><parent_chain><item><author>matthewcanty</author><text>That was a really interesting read, and very well written. I wonder if anyone can clear this up though...&lt;p&gt;I find the terminology of open and closed intervals contradictory to their meaning. Does anyone know why they are described like this?&lt;p&gt;`Closed` makes me think shut or not-including - however it includes its endpoints. `Open` makes me think inclusive - yet does not include its endpoints.</text></item></parent_chain><comment><author>jdpage</author><text>From a real analysis standpoint... the definition of a &amp;#x27;closed set&amp;#x27; in an N-dimensional metric space (of which Euclidean space, i.e. normal space, is an example) is as follows: a set C is &amp;#x27;closed&amp;#x27; if and only if, given any sequence of elements (x_n) converging on x, such that (x_n) is a subset of C, it follows that x is also in C.&lt;p&gt;Under this definition, &amp;#x27;closed&amp;#x27; makes sense in the larger context, since in mathematics, if an operation is &amp;#x27;closed&amp;#x27; on a set, that means that applying the operation to elements of the set always yields another element of the same set.&lt;p&gt;Open is a bit more awkward. A set O is &amp;#x27;open&amp;#x27; if and only if the complement of O (i.e. the set of all points not in O) is closed. So open is kind of the opposite of closed, hence the convention. Of course, it isn&amp;#x27;t really the opposite of closed, since there are sets which are neither closed nor open.&lt;p&gt;tt;dr (too technical; didn&amp;#x27;t read) in maths, &amp;#x27;closed&amp;#x27; usually means &amp;#x27;I can do stuff inside this set without falling out of it&amp;#x27;. In the case of intervals, the &amp;#x27;stuff&amp;#x27; in question is taking a limit of a convergent sequence.</text></comment>
<story><title>Cryptic genetic variation in software: hunting a buffered 41-year-old bug</title><url>https://cryptogenomicon.wordpress.com/2014/10/13/cryptic-genetic-variation-in-software-hunting-a-buffered-41-year-old-bug/</url></story><parent_chain><item><author>matthewcanty</author><text>That was a really interesting read, and very well written. I wonder if anyone can clear this up though...&lt;p&gt;I find the terminology of open and closed intervals contradictory to their meaning. Does anyone know why they are described like this?&lt;p&gt;`Closed` makes me think shut or not-including - however it includes its endpoints. `Open` makes me think inclusive - yet does not include its endpoints.</text></item></parent_chain><comment><author>saurik</author><text>The analogy I&amp;#x27;ve always used is that the closed interval has what amounts to a lid or a cap on it, while the open interval does not. Another (sort of related) way of looking at it is that the closed interval has a maximum (or minimum) value, whereas the open interval, despite only missing a single value, suddenly has this feeling of continuation, because without that final value it now asymptotes to the end and you will always be able to find a larger (or smaller) value than any previous value you examine.</text></comment>