Teorema de Bolzano-Weierstrass

The Bolzano-Weierstrass theorem states that any bounded sequence of numbers (meaning the numbers stay within a certain range) must have at least one subsequence that gets closer and closer to a specific value, called a limit point. In simpler terms, if you have a list of numbers that doesn't go off to infinity or negative infinity, then you can always find a smaller list inside it that converges to some particular number. This property is fundamental in understanding the behavior of sequences in mathematical analysis.