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A basic example of functional decomposition is expressing the four binary arithmetic operations of addition, subtraction, multiplication, and division in terms of the two binary operations of addition <math>a + b</math> and multiplication <math>a \times b,</math> and the two unary operations of additive inversion <math>-a</math> and multiplicative inversion <math>1/a.</math> Subtraction can then be realized as the composition of addition and additive inversion, <math>a - b = a + (-b),</math> and division can be realized as the composition of multiplication and multiplicative inverse, <math>a \div b = a \times (1/b).</math> This simplifies the analysis of subtraction and division, and also makes it easier to axiomatize these operations in the notion of a [[Field (mathematics)|field]], as there are only two binary and two unary operations, rather than four binary operations.
Extending these primitive operations, there is a rich literature on the topic of [[
===Example: Decomposition of continuous functions===
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