\(\forall \epsilon > 0\),

• \(\exists \delta > 0\), 使得当\(|x - x_0| < \delta\)时, \(|f(x) - A| < \epsilon\)成立: \(\lim_{x \to x_0}f(x) = A\)
• \(\exists X > 0\), 使得当\(|x| > X\)时, \(|f(x) - A| < \epsilon\):\(\lim_{x \to \infty} f(x) = A\).

数列极限在形式上可以看作第二种情况的特殊形式.