complex.docx
complex.pdf
The Gauss plane of complex numbers is of 2 dimension with the real axis and the imajinary axis or the basis is [1,i].

Can we extend this to the  3 dimensional field with basis 1,i and j?

We show it is not the case.

 

isomorphism=one-to-one and  onto

 

 

Suppose X is a  complex topological vector space, Y is a subspace of X, and dimY=n.

Then every isomorphism of C^n onto Y is a homemorphism , and Y is closed.

A metric d is invariant if

d(x+z,y+z)=d(x,y) for all x,y,z

a continuous mapping whose inverse is also continuous
intg_sin.gif

Euler 1707-1783

Gauss 1777-1855

 

Formulas must not be proved. but must be founded out.

 

For example

euler1.gif

 

 

 

 

or

euler2.gif

 

 

 

 

 Any number of formulas can be founded out one after another.

These are called Euler integrals, particularly containing Gamma function and Beta function. 

 

dx とdy の解析学

オイラーに学ぶ

高瀬 仁著

日本評論社

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