Is it fair to suggest that the fact a base's symbol which would exist in a higher base but is never truly reflected in the base itself is an example(see below) of incompleteness along the ideas of the theorems? My apologies as I'm mostly self-teaching in these areas and feel I've skipped a lot of interim understanding. I don't know logic notation yet so can't follow any raw work. My example would be as follows;
In binary, base 2, we only ever feature the numbers 0 and 1 in all our numerical representations. Despite the fact it's base 2 the numerical symbol of 2 itself never actually appears in this system as this is instead 10.
Is this an example of the theories of incompleteness? Have I just made a random naive or arbitrary correction or is this a fair conclusion of sorts, if even very simplistic? Thanks in advance.
Incompleteness (in the logical sense) is not about representation of mathematical objects. Rather, it concerns the relation of truth and provability in mathematics, where the latter concepts are understood in a specific technical sense.
There is no good metaphor which fully capture it. Douglas Hofstadter made an attempt in Gödel, Escher, Bach: An Eternal Golden Braid, which I recommend.
My advice is to begin by learning formal logic. Otherwise, it will be like trying to understand quantum physics without learning calculus or any other physics.