Negate "f has limit L at c": f does not have limit L at c

[soulflyfgm]

I found this in another threat
however i do not know wat he means by convergent sequences. Is something like when u trying to take the limit at an ASYMPTOTE of a fuction? i know that the limit doesn't not exist( or goes to infinitive i cannot recall) is that wat he means by convergent sequence?

Let f:I->R and let c in I. I want to negate the statements: "f has limit L at c" and "f is continuous at c". Are these correct?

f does not have limit L at c if there exists e>0 such that for some sequence {x_n} converging to c, |f(x_n)-L|>e for every n.

f is not continuous at c if there exists e>0 such that for some sequence {x_n} converging to c, |f(x_n)-f(c)|>e for every n.

edit: also, what is the negation of "f has a limit at c"?

 

[fourier jr]

the negation of "f has a limit at c" is "f does not have a limit at c". (meaning there is no L such that blah blah)

for the one about the sequence f is not continuous at c if for some x in I, $$\lim_{x\rightarrow c}f(x) \neq f(c)$$. that is... well you know the definiton of limit, & if not it's in your book. of course if there's one x where f isn't continuous then if isn't continuous on the domain.

 

[tacman]

The negation of "f has a limit at c" is "f does not have a limit at c". This means that there does not exist a finite number L such that for any sequence {x_n} converging to c, the limit of f(x_n) as n approaches infinity is equal to L. Essentially, this means that the function does not approach a specific value as the input approaches c.