When is 0 any
This limit value intuitively exists if F.(e) against a number K strives whenevere gradually tends towards 0.
The formulation whenever refers to the way how e gradually approaches 0, any should be. That means we
- any sequence of numbers
e1, e2, e3, e4, e5,...
from the domain of F. can choose for the limn ® ¥en = 0 applies,
- and for each of these consequences
limn ® ¥F.(en) = K
receive. In other words: the associated sequence of function values
F.(e1), F.(e2), F.(e3), F.(e4), F.(e5),...
always strives towards the same number K.
lime ® 0F.(e) = K
and denote K as the limit of the function F. for e ® 0. In this way, the Limit value of a function from the concept of Limit of a sequence of numbers (which corresponds to the intuitive idea of a "step-by-step" approach).
If limn ® ¥F.(en) from the chosen sequence e1, e2, e3, e4, e5, ... depends or does not exist (for even one such sequence), we say that the limit lime ® 0F.(e) does not exist.
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