tag:blogger.com,1999:blog-3748625510348961342.post6869702865840300655..comments2020-08-05T05:44:35.592-07:00Comments on solidangl.es: Infinity is my favorite number.Bill Shillitohttp://www.blogger.com/profile/17774101901445053590noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3748625510348961342.post-86316962816040050712014-09-16T15:05:43.056-07:002014-09-16T15:05:43.056-07:00I wouldn't call it a "huge mathematical b...I wouldn't call it a "huge mathematical blunder". The contradiction reached was intentional - the point was to show that an apparent "fact" about numbers may only actually work in particular situations. In the case of \(\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\), this is only guaranteed to work as long as \(a\) and \(b\) are positive real numbers — if we try to work with negative reals or complex numbers, the equation no longer holds, as you pointed out. (Do keep in mind, though, that when working with positive reals, the symbol \(\sqrt{x}\) only refers to the positive root of \(x\)!)Bill Shillitohttps://www.blogger.com/profile/17774101901445053590noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-20860610595245536482014-09-16T13:41:05.500-07:002014-09-16T13:41:05.500-07:00My reply has not shown up? Bill Shillito, you mad...My reply has not shown up? Bill Shillito, you made a huge mathematical blunder in your argument concerning i. Even root radical equations can have extraneous roots, the sqrt(1) is actually + or - 1 with +1 being the extraneous root. shutup_and_just_drink_beerhttps://www.blogger.com/profile/18408390216090324892noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-14544575846404342014-09-15T21:01:10.597-07:002014-09-15T21:01:10.597-07:00I love your responses to my posts. :DI love your responses to my posts. :DBill Shillitohttps://www.blogger.com/profile/17774101901445053590noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-39716626859345865142014-09-15T20:52:06.545-07:002014-09-15T20:52:06.545-07:00Those who claim that Infinity is Not A Number need...Those who claim that Infinity is Not A Number need to read their standards more carefully. According to IEEE-754, single precision (positive/negative) Infinity is the bitstring (0/1)1111111100000000000000000000000, while single precision Not A Number is any bitstring which differs from this one in any of the last 23 bits. Yes, that's right, IEEE-754 defines Not A Number in terms of what differentiates it from Infinity, thus definitively proving that Infinity cannot be Not A Number.Quintopiahttps://www.blogger.com/profile/11935053984682797775noreply@blogger.com