an epsilon of room i real analysis graduate studie
such that if \(0 < |x - a| < δ\), then \(|f(x) - L| < ε\). This definition captures the essence of a limit: that the values of \(f(x)\) can be made arbitrarily close to \(L\) by choosing \(x\) sufficiently close to \(a\). Implications for Graduate Studies: Mastery of this definition i