constructing the reals

Summary

The real numbers can be explicitly constructed as sets of rational numbers using the Dedekind cut construction.

Context

This concept has the prerequisites:

Goals

  • Define the real numbers using the Dedekind cut construction.
  • Show that this construction satisfies the least upper bound property.
  • Define the basic arithmetic operations and comparison operators
  • Show that these satisfy the field axioms

Core resources (read/watch one of the following)

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See also

-No Additional Notes-