I mean why would someone deliberately create such confusing definition of limits. Why would existance of delta affects epsilon, why in proof can i put any value of delta (usually 1) and then i have to overwrite that to delta = min {1, something}. Also, proof of any question that says to prove the limit of this fx is (insert number), does not make any sense. Please explain.
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> such confusing definition of limits
It’s only confusing because you aren’t familiar with it. In reality, it’s *rigorous* and provides a way for mathematicians to precisely describe what it means for a limit to exist.
The simplest way to wrap your head around it is like this: someone hands you an interval on the y-axis, called epsilon. Whatever that interval is, you need to be able to choose an interval on the x-axis, called delta, small enough that *for x values within the interval delta, all of the y-values are within the interval epsilon*. When you set delta to the minimum of two things, it’s usually because e.g. 1 is “good enough” for large values of epsilon, but you need smaller x-intervals for smaller values of epsilon.
Without a concrete example to work through, it’s hard to give a better explanation than that. The point is that you want to choose your delta so that for any x value you pick, the value of f(x) is within epsilon of your limit.
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