In ordinary math, the infinite decimal .999… is defined to be the limit of the terminating decimals .9, .99, .999, …; that is, it’s defined to be the real number that the fractions 9/10, 99/1…| mathenchant.wordpress.com
“Think about the knife tip. That is where you are. Now feel with it, very gently. You’re looking for a gap so small you could never see it with your eyes, but the knife tip will find it, if you put…| mathenchant.wordpress.com
There’s a pretty thought experiment that’s sometimes attributed to Democritus though it’s actually due to a later popularizer of the atomic hypothesis1 and it goes like this: Suppose we use the wor…| mathenchant.wordpress.com
dedicated to Norman Skliar and Sidney Cahn In an earlier blog-essay, When 1+1 Equals 0, I explained how 1 + 1 = 0 makes sense in mod 2 arithmetic; today I’ll tell you how the equation 1 + 1 = 1 mak…| mathenchant.wordpress.com
John McWhorter, one of my favorite public intellectuals, writes (in his recent essay “Lets chill out about apostrophes”), “Writing does not entail immutable rules in the way that mathematics does.”…| mathenchant.wordpress.com
No reckoning allowed save the marvelous arithmetics of distance (from Smelling the Wind by Audre Lorde) Suppose a child comes up to you and says “I know 1 is odd and 2 is even, but I think 4 is mor…| mathenchant.wordpress.com
How far would you go to save a theorem? Would you invent a new kind of number? That’s what the mid-19th century German mathematician Ernst Eduard Kummer did, and while he was partly driven by the h…| mathenchant.wordpress.com
To err is human; we all make mistakes. But some mistakes have worse consequences than others. According to Greek myth, King Sisyphus of Ephyra made the especially big mistake of cheating Hades, the…| mathenchant.wordpress.com
