How to construct a field that is larger than the complex numbers $\mathbb{C}$?
In this article, we discuss the following questions:Can we extend the complex numbers in any way such that $\mathbb{C} \subset\mathbb{C}[a]$ ? Or is $\mathbb{C}$ the extension to end all extensions?Surrounding these questions, we will provide two methods that extend the complex field $\mathbb{C}$.Method 1: The cartesian product of fields $$P = {\Bbb C}\times{\Bbb C}\times\cdots$$ isn't a field because has zero divisors: $$(0,1,0,1,\cdots)(1,0,1,0\cdots)=(0,0,0,0,\cdots).$$But a quotient will be ...