Use the Bolzano-Weierstrass theorem to show that R is complete. The following proposition is regarded as the

Question:

Use the Bolzano-Weierstrass theorem to show that R is complete.
The following proposition is regarded as the most important theorem in topology. We give a simplified version for the product of two metric spaces. By induction, it generalizes to any finite product. In fact the theorem is also true of an infinite product of compact spaces.