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**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.