Claire Xen  🏳️‍⚧️ 🏳️‍🌈 🧙🏻‍♀️ BLM  🏴 🚩

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.

e.g. forbidden word problems. If 0.101111... and 0.110000... are the same, then it's difficult to say that the first avoids the forbidden word '000' if the second is in some way identical to it. (just an ex. off the top of my head)

PS - this is probably the *least* weird thing about Algorithmic Randomness x-D

Excuse my ignorance. I've just read a bit on the topic on wikipedia. I'm mostly confused now. :) Most reals famously don't even have a finite description. So I have a hard time understanding how these questions even relate to those reals. If only I had more time. This looks cool.

so, being honest with you - you can do just fine with these problems if you don't think of them as anything more than binary strings, i.e. you don't think of them as reals. >.< I'm very sorry if I've caused confusion...

I think this is a case where being mathematicians, we state something to avoid confusion later, but instead cause even more confusion at the start. We're rather good at that...

Confusion just means I know there's something to learn for me. That's usually good. :) So, when you say these objects are "binary strings", these strings are still potentially infinite in length, and for most of them there's no finite program to generate them, right?

Exactly. Much of the study is for $\Pi^0_1$ classes, meaning there is some arithmetical function $\phi$, and we are saying $\forall x \, \phi(x)$ is true. After some work, this becomes equivalent to the usual interpretation: