Taken from wiki on “Limit of a function”.
“Formal definitions, first devised in the early 19th century, are given below.
Informally, a function fassigns an
output f(x) to every input x. We say that the function has a limit L at an input p, if f(x) gets closer and closer to L as x moves closer and closer to p. More specifically, when f is applied to any input sufficiently close to p, the output value is forced arbitrarily close to L. On the other hand, if some inputs very close to p are taken to outputs that stay a fixed distance apart, then we say the limit does not exist”
only in the wiki the words “sufficiently” and “arbitrarily” are italicized. Rightly so?