I know I've posted this before. I don't remember it getting any traction with y'all. But it's relevant to my struggles with beliefs in potential vs actual infinity:
Belief in the Sinularity is Fideistic https://link.springer.com/chapter/10.1007%2F978-3-642-32560-1_19 Not unrelated, I've often been a fan of trying identify *where* an argument goes wrong. And because this post mentions not only 1/0, but Isabelle, Coq [⛧], Idris, and Agda, I figured it might be a good follow-up to our modeling discussion on Friday, including my predisposition against upper ontologies. 1/0 = 0 https://www.hillelwayne.com/post/divide-by-zero/ Here's the (really uninformative!) SMMRY L7: https://smmry.com/https://www.hillelwayne.com/post/divide-by-zero/#&SM_LENGTH=7 > Since 1 0, there is no multiplicative inverse of 0⁻. Okay, now we can talk > about division in the reals. > > So what's -1 * π? How do you sum up something times? While it would be nice > if division didn't have any "Oddness" to it, we can't guarantee that without > kneecapping mathematics. > > We'll define division as follows: IF b = 0 THEN a/b = 1 ELSE a/b = a * b⁻. > > Doing so is mathematically consistent, because under this definition of > division you can't take 1/0 = 1 and prove something false. > > The problem is in step: our division theorem is only valid for c 0, so you > can't go from 1/0 * 0 to 1 * 0/0. The "Denominator is nonzero" clause > prevents us from taking our definition and reaching this contradiction. > > Under this definition of division step in the counterargument above is now > valid: we can say that 1/0 * 0 = 1 * 0/0. However, in step we say that 0/0 = > 1. > > Ab = cb => a = c but with division by zero we have 1 * 0 = 2 * 0 => 1 = 2. [⛧] I decided awhile back to focus on Coq because it seems to have libraries of theorems for a large body of standard math. But still NOT having explored it much, yet learning some meta-stuff surrounding the domain(s), I'm really leaning toward Isabelle. I suppose, in the end, I won't learn to use any of it, except to pretend like I know what I'm talking about down at the pub. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
