Bolzano-Weierstrass Theorem

The Bolzano-Weierstrass theorem states that any bounded sequence of numbers (like a list that doesn’t go off to infinity) will always have at least one subsequence that converges to a specific value. Essentially, if you have a set of numbers that stay within certain limits, you can find a smaller part of that set that zeroes in on a particular number as you keep looking further out in the sequence. This theorem is important in mathematics for understanding limits and continuity, serving as a foundational concept in calculus and analysis.