👉 Cuts math, also known as the Cuts Theorem, is a fundamental result in real analysis that provides a rigorous framework for understanding the continuity and differentiability of functions. It states that given a function \( f \) defined on an open interval \( (a, b) \), if the limit of \( f(x) \) as \( x \) approaches \( c \) exists and equals \( L \), then for any \( \epsilon > 0 \), there exists a \( \delta > 0 \) such that whenever \( |x - c| < \delta \), it follows that \( |f(x) - L| < \epsilon \). This essentially means that small changes in the input \( x \) near \( c \) result in small changes in the output \( f(x) \), with the limit \( L \) being a precise threshold. The cuts math formalizes the intuitive notion of continuity by ensuring that the function's value at a point \( c \) can be approximated arbitrarily closely by the limit of its values at nearby points, thus bridging the gap between the local behavior of functions and their global properties.
