It isn't that I'm changing "specified" to "known"; I'm pointing out that this is an article on a purported "encyclopedia of unknowns," and it's only being included there because the authors clearly view these as "unknowable" in some sense.
The thing you are calling "repeating-digits shorthand" is a highly nontrivial thing. It essentially equates to an algorithm that gives you the N'th decimal digit of the expansion for any N you want.
It does so happen that 1/7 has an extremely simple pattern - it's just the same six digits repeating, so you can take N mod 6 and immediately know what the digit is.
But there are plenty of irrational numbers which have similarly simple patterns, such as the Champernowne constant(https://en.wikipedia.org/wiki/Champernowne_constant), whose decimal expansion is just the concatenation of the decimal expansion of every integer: 0.123456789101112131415... . This is an irrational number, but it's a trivial programming 101 exercise to write a basic algorithm that can give you the N'th digit in the decimal expansion.
The same thing is true for e.g. sqrt(2) and pi. These numbers have decimal expansions that would seem to be random and chaotic at first glance, but are really not - there is again another pattern there. For instance, there exist "spigot" algorithms that can give us the N'th digit in the decimal expansion of pi without having to compute any of the previous digits, because it utilizes such a pattern that is simply a bit less readily seen and perceived by human beings, but is still there.
All of these numbers can easily be "known" in the sense that you can know as many digits as you want, whenever you want. Uncomputable numbers are the numbers for which this is not true.
The thing you are calling "repeating-digits shorthand" is a highly nontrivial thing. It essentially equates to an algorithm that gives you the N'th decimal digit of the expansion for any N you want.
It does so happen that 1/7 has an extremely simple pattern - it's just the same six digits repeating, so you can take N mod 6 and immediately know what the digit is.
But there are plenty of irrational numbers which have similarly simple patterns, such as the Champernowne constant(https://en.wikipedia.org/wiki/Champernowne_constant), whose decimal expansion is just the concatenation of the decimal expansion of every integer: 0.123456789101112131415... . This is an irrational number, but it's a trivial programming 101 exercise to write a basic algorithm that can give you the N'th digit in the decimal expansion.
The same thing is true for e.g. sqrt(2) and pi. These numbers have decimal expansions that would seem to be random and chaotic at first glance, but are really not - there is again another pattern there. For instance, there exist "spigot" algorithms that can give us the N'th digit in the decimal expansion of pi without having to compute any of the previous digits, because it utilizes such a pattern that is simply a bit less readily seen and perceived by human beings, but is still there.
All of these numbers can easily be "known" in the sense that you can know as many digits as you want, whenever you want. Uncomputable numbers are the numbers for which this is not true.