the 8/2(2+2) crowd is almost as annoying as the people who claim that 9.99999... and 10 are different numbers and equally annoying as the people who can't grasp that dividing by zero is as invalid in algebra as it is in arithmetic send tweet
-
Fun aside - in Algorithmic Information theory, you do want binary strings like 10.111111... and 11.0000... to be different, so a common convention to avoid confusion in Cantor space is to treat all binary reals as irrational. (Photo snapped from my copy of Downey and Hirschfelt)pic.twitter.com/ehO9WDVWUz
Interesting. Not sure if I'm missing something here, but 11.0000... obviously is rational. Therefore, as far as I understand this, it's not assuming that 10.1111... and 11.0000... are different. Instead, it's assuming that we never encounter such numbers.
-
-
Okay, I read it again.. :) I'd need to know more about the problems studied here, but assuming that natural numbers are irrational intuitively screams huge bag of problems. I trust that it's not an actual problem in this case.
-
Yeah, it's only an issue when you want to have a set of positive measure to show a binary string in ML-Random, or when you want to work on subshifts (sets closed under the 'shift left one' operation) and need everything to be distinct points without such identities creeping in.
- Show replies
New conversation -
-
-
it's more to avoid issues with boundaries of closed sets - which in Cantor space are trees. You definition of measure can get gnarled up without the assumption that all reals are irrational...
-
Additionally, it's not good to have the left-most and right-most paths thorough adjacent trees be the same points. It only becomes important in the theory of $\Pi^0_1$ classes (which are trees, in the 'closed under substring' sense in Cantor and Baire space)
- Show replies
New conversation -
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.