# An example of incompleteness?

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.

• "random naive" seems to sum it up pretty well. – Gerry Myerson Mar 19 at 11:16
• The word incompleteness,as it is usually used, doesn't have much to do with symbols – Max Mar 19 at 11:16
• "Is this an example of the theories of incompleteness?" No. It has nothing at all to do with incompleteness in the logical sense. The binary number system is perfectly capable of expressing all natural numbers. There is nothing surprising in the observation that in any base, there is a limit to what can be expressed with a single digit number. On the other hand, the incompleteness theorems were very surprising indeed. – John Coleman Mar 19 at 11:18
• Having said that, there is a weak analogy in what you suggest, and analogies, even if weak, can potentially aid intuition, as long as you don't press the analogy too far. – John Coleman Mar 19 at 11:29
• You are conflating objects and symbols. The number two is the object that has the symbol $2$ as name in the decimal system and the symbol $10$ as name in the binary system. – Mauro ALLEGRANZA Mar 19 at 13:01