Terminology – What Does ‘Formal’ Mean?

soft-questionterminology

I know the definition of formal power series, power series and polynomials. But what does the adjective "formal" mean? In google English dictionary, does it mean "9. Of or relating to linguistic or logical form as opposed to function or meaning" or maybe another one in the link?

Or does "formal" have some mathematical meaning which is other than usual dictionary meaning?

Best Answer

I see formal used in at least two senses in mathematics.

  • Rigorous, i.e. "here is a formal proof" as opposed to "here is an informal demonstration."
  • "Formal manipulation," that is, manipulating expressions according to certain rules without caring about convergence, etc.

Confusingly they can mean opposite things in certain contexts, although "formal manipulations" can be made rigorous in many cases.

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