There are several things to be careful of here both in real problems in science and in abstract problems in mathematics. In science the usual warnings about units hold as in the previous example. It may look OK to say where and are both in meters and then to form , but the latter has a power series expansion and is dimensional nonsense. In mathematics one has to worry about the domain and range (defined below when we talk about functions). Suppose I have the relation where is a real dimensionless expression, and I wish to take the of both sides. Well, the range of cosine is only to , and my function is clearly strictly larger than 2.