 A concept that is closely related to idealization is approximation. In a broad sense, A can be called an approximation of B if A is somehow close to B. This, however, is too broad because it makes room for any likeness to qualify as an approximation. Rueger and Sharp (1998) limit approximations to quantitative closeness, and Portides (2007) frames it as an essentially mathematical concept. On that notion A is an approximation of B iff A is close to B in a specifiable mathematical sense, where the relevant sense of “close” will be given by the context. An example is the approximation of one curve with another one, which can be achieved by expanding a function into a power series and only keeping the first two or three terms. In different situations we approximate an equation with another one by letting a control parameter tend towards zero (Redhead 1980). This raises the question of how approximations are different from idealizations, which can also involve mathematical closeness. Norton (2012) sees the distinction between the two as referential: an approximation is an inexact description of the target while an idealization introduces a secondary system (real or fictitious) which stands for the target system (while being distinct from it). If we say that the period of the pendulum on the wall is roughly two seconds, then this is an approximation; if we reason about the real pendulum by assuming that the pendulum bob is a point mass and that the string is massless (i.e., if we assume that the pendulum is a so-called ideal pendulum), then we use an idealization. Separating idealizations and approximations in this way does not imply that there cannot be interesting relations between the two. For instance, an approximation can be justified by pointing out that it is the mathematical expression of an acceptable idealization (e.g., when we neglect a dissipative term in an equation of motion because we make the idealizing assumption that the system is frictionless).