Where Can I Learn About the Construction of Number Systems?

[BustedBreaks]

I was wondering if someone could recommend a good text that explains the construction of complex from real, real from rational, rational from integers, and integers from natural numbers.

Thanks

 

[Petek]

Here are two books that cover what you asked for:

https://www.amazon.com/dp/082182693X/?tag=pfamazon01-20 by Edmund Landau

https://www.amazon.com/dp/0486458067/?tag=pfamazon01-20 by H. A. Thurston

Landau's book is well-known. However, as some of the Amazon reviews point out, it is extremely dry. It contains little, if any, motivational material and no exercises.

Thurston, on the other hand, consists of approximately one-half motivational material and one-half formal definitions, theorems and proofs. It also contains exercises, but no solutions.

Landau uses Dedekind cuts to define the real numbers, while Thurston uses Cauchy sequences. Both approaches are valid, but the Dedekind cuts approach is probably more commonly seen elsewhere.

So, you might want to see if your library has both books and decide which one you like the most.

Petek

 

[BustedBreaks]

Here are two books that cover what you asked for:

https://www.amazon.com/dp/082182693X/?tag=pfamazon01-20 by Edmund Landau

https://www.amazon.com/dp/0486458067/?tag=pfamazon01-20 by H. A. Thurston

Landau's book is well-known. However, as some of the Amazon reviews point out, it is extremely dry. It contains little, if any, motivational material and no exercises.

Thurston, on the other hand, consists of approximately one-half motivational material and one-half formal definitions, theorems and proofs. It also contains exercises, but no solutions.

Landau uses Dedekind cuts to define the real numbers, while Thurston uses Cauchy sequences. Both approaches are valid, but the Dedekind cuts approach is probably more commonly seen elsewhere.

So, you might want to see if your library has both books and decide which one you like the most.

Petek

Thanks, I think I'll pick up Thurston's book eventually.

Any online texts?