real number l
[real number l|real number l] The limit of f(x) at a does not exist if for every real number L, there exists a real number ε > 0 such that for all δ > 0, there is an x satisfying 0 < |x - a| < δ and |f(x) - L| > ε.
Definition
real number l The limit of f(x) at a does not exist if for every real number L, there exists a real number ε > 0 such that for all δ > 0, there is an x satisfying 0 < |x - a| < δ and |f(x) - L| > ε.
Mechanism
The real number L represents the limit of f(x) as x approaches a from the left or right, depending on whether x values approach a from below or above. real number l is determined by the function's behavior near a, with left-hand limits involving x < a and right-hand limits involving x > a.
Causes
real number l is the limit of f(x) as x approaches a from the left when f(x) approaches L from values of x less than a. Similarly, it is the limit as x approaches a from the right when f(x) approaches L from values of x greater than a.