The Bolzano-Weierstrass theorem is a fundamental result in real analysis and states that each infinite bounded real sequence has a convergent subsequence. Also, it has some applications in data science and economics. In order to prove the Bolzano-Weierstrass theorem, first we need to prove a result called the monotone subsequence theorem. Note that the monotone…

# Tag: converging sequences

## Convergent real sequences

Convergent real sequences play a crucial role in mathematics for data science. In this post, we will first define real sequences and their convergence. We, then, list some basic properties of convergent real sequences. Finally, we give some examples to clarify the crucial points related to the convergence of real sequences. Convergent real sequences Definition…