Approximate computing is gaining more and more attention as potential solution to the problem of increasing energy demand in computing. Several recent works focus on the application of deterministic approximate computing to arithmetic computations. Circuits for addition and multiplication are simplified, trading exactness for energy and/or speed. Recent approximation techniques for adders focus on modifications of individual full adders' truth tables or shortening carry chains. While the resulting error is usually characterized with statistical measures over the range of possible input/output combinations, the actual adder is a static nonlinear system regarding arithmetic operations and signal processing. The resulting unexpected effects present a challenge for adopting approximate computing as a widespread and standard application-level optimization technique. This paper focuses on the deterministic effects of approximate multi-bit adders, which are especially evident for certain input data in an otherwise well specified systems, showing the necessity to look beyond purely statistical measures. We show which fundamental principles are violated depending on the chosen approximation scheme, and how this choice affects practical applications. This can serve as a basis for designers to make informed decisions about the use of approximate adders at the application level.