# Talk:Turinf machine

The missing syntax for halting states was an oversight, thanks for spotting that. Regarding the Turing-completeness: maybe the specification was not clear enough (I reworded it, hope it is better now), but the whole point is that not all Turinf machines can be output by Turing machines. Some Turinf machines have states that cannot be defined by any algorithm that has a finite number of symbols. Here is an analogy with real numbers on interval ${\displaystyle \left[0,1\right)}$: since each real number on that interval can be encoded as an infinite string of binary digits, each such real number corresponds to a single Turinf machine program. Some of the real numbers (like Chaitin's constants) are uncomputable (there is no algorithm that outputs their digits), thus there is no Turing machine that can generate some Turinf machines. Being able to directly encode all digits of a Chaitin's constant (which is possible in a Turinf machine) allows us to solve the halting problem for any Turing machine. --Hakerh400 (talk) 15:11, 6 August 2020 (UTC)