> An alternative view is that any C "unsigned" is both positive and negative. For example the unsigned short "1" is the same number as "65537" and as "-65535".

This can be disproven by the fact that dividing by `unsigned e = 1U` is well defined and always yields the starting number. If the unsigned numbers were really modular numbers as you suggest, division could not be defined.

This does not demonstrate anything. It is just additional evidence that the C standard contains contradictory rules about "unsigned" integers.

The oldest parts of the C language are all consistent with "unsigned" numbers being non-negative integers. The implicit conversions between different sizes of "unsigned", the sizeof operator, the relational operators and division are consistent with non-negative integers.

However the first C standard, instead of defining the correct behavior has left undefined many corner cases of the arithmetic operations, allowing the implementation of "unsigned" as either non-negative integers or integer residues.

Eventually, the undefined behaviors for addition, subtraction and multiplication have been defined to be those of integer residues, not those of non-negative integers.

These contradictory properties are the cause of many confusions and bugs.

In extensible languages, like C++, it is possible to define proper non-negative integers and integer residues and bit strings and to always use those types instead of the built-in "unsigned".

In C, it is better to always use signed numbers and avoid unsigned, by casting unsigned to bigger sizes of signed before using such a value.