This is something elementary, so I need to have a practical notion as well as a theoretical one for definitions and theorems that include a positive epsilon number $(\epsilon >0)$.
What does this number mean, how is it interpreted?
In the following definition, how do I visualize or imagine $\epsilon$?
For example, the next is taken from Amemiya(1994) "Introduction to Statistics and Econometrics"
DEFINITION 6.1.1 Asequence of real numbers {$\alpha_{n}$}, n = 1, 2, . . . , is said to converge to a real number $\alpha$ if for any $(\epsilon >0)$ there exists an integer N such that for all n > N we have
$|\alpha_{n}-\alpha|<\epsilon$
. . . Thanks
