Hey Veeky Forums, i have a question about limits

Depends on if the function converges uniformly or not. If not, you lose information and can't reverse the process.

is there no way to extract that information?

just nonsense

no

all you have is a point and its neighborhoods. you have no idea which way you came through

No an angle can't be considered as *a* convergence. There are many different motions of the door that lead to the status door=closed, meaning you can give the door different speeds and accelerations, etc. etc.

Of course you can identify a value with the set of all sequences converging to it, but that's fucking pointless.

not even with...point set topology and functional analysis having a baby or something?

>What i want to know is, can a vertical line be mathematically unwrapped or deconstructed to show that the converse is true? that a vertical line diverges to a curve? Is there a duality for such a thing? Can a series be shown that it converges to a value, and that conversely, the value can be used with some initial value or bound of an equation so that it tapers or "expands" out into the function or series you originally were discussing as being convergent to a limit?

Yeah, see the heat equation with an impulse starting condition.

are you just saying the names of courses you haven't taken yet, but will have to take in 2 years?

nah holmes i just think that they might help, i mean isn't toplogy aboute the correlation of points and their neighbourhoods, and trying to extrapolate an underlying structure with as little initial detail as possible?

it can, but not uniquely.
see convergence as a funnel.
water goes in and is pushed to a point.
If you send water through the funnel the other way around, its not pushed and will show some behaviour other than convergence.

i have a pre-university level of understanding of mathematics so i dont know how to attack this question mathematically

however, it seems to me that in the case trying to make defining the limit of a curve reversible you run into the problem of information loss.

there are an infinite number of curves that converge into a line. you cannot possibly know which curve a line you are looking at was derived (as it were) from.

someone who understands entropy and information theory could give you a more rigorous answer but to be honest it seems pretty fucking obvious that its not reversible if you are just given a line drawn on a piece of paper for gods sake