Fields

It is a well known fact that the set of real numbers form a field.The n-dimensional real space viewed as a vector space is a group under addition but with a given multiplication rule for makes them real and complex fields respectively.Is this “rule of multiplication” unique? In other words is there any other multiplication rule other than         to make a field?? On the other hand is there any multiplication rule for to make it a field for ?

Inspiring moments

It is a basic principle in the study of mathematics, and one too seldom emphasized, that a proof is not really understood until the stafe is reached at which one can grasp it as a whole and see it as a single idea.In achieving this end,much more is necessary than merely following merely individual steps in the reasoning.This is only the beginning.A proof should be chewed,swallowed, and digested, and this process of assimilation should not be abandoned until it yields a full comprehension of the over all pattern of thought.

-An extract from a book on topology and analysis.

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