Editing Computable number (section)

==Informal definition==
In the following, [[Marvin Minsky]] defines the numbers to be computed in a manner similar to those defined by [[Alan Turing]] in 1936;{{sfnp|Turing|1936}} i.e., as "sequences of digits interpreted as decimal fractions" between 0 and 1:{{sfnp|Minsky|1967}}
 
{{Blockquote|text=A computable number [is] one for which there is a Turing machine which, given ''n'' on its initial tape, terminates with the ''n''th digit of that number [encoded on its tape].}}

The key notions in the definition are (1) that some ''n'' is specified at the start, (2) for any ''n'' the computation only takes a finite number of steps, after which the machine produces the desired output and terminates.

An alternate form of (2) – the machine successively prints all ''n'' of the digits on its tape, halting after printing the ''n''th – emphasizes Minsky's observation: (3) That by use of a Turing machine, a ''finite'' definition – in the form of the machine's state table – is being used to define what is a potentially ''infinite'' string of decimal digits.

This is however not the modern definition which only requires the result be accurate to within any given accuracy. The informal definition above is subject to a rounding problem called the [[table-maker's dilemma]] whereas the modern definition is not.