What is the difference between "Field" and "Set"? I was browsing through the Notation section of my favourite book and noticed that symbols were defined for the "sets" of real, integer and natural numbers... but for the "field" of complex numbers. Is the terminology different because a complex number comprises two components (real and imaginary)? I don't want a cripplingly in-depth definition - Wikipedia tells me a field is a "commutative ring whose nonzero elements form a group under multiplication". This means almost nothing to me.