Why did retarded mathematicians invent something as stupid as limits? This is the most amibguous shit I have ever been forced to learn. Even when trying to PROVE that a limit for a certain series exists, the proof just suddenly stops and q.e.d. Then you just whatever the fuck you want for your inputs and you're done. Circulatory logic at its finest. If only maths were the domain of engineering, then everything would have nice and clean order. Thanks for nothing, math-FAGS!
Yeah and this is what gets me. We use epsilon-N/epsilon-n0 however and the annoying part is that this kind of proof is not very concrete in its nature. At the end of the proof you still have the freedom to chose N, n and epsilon as you wish so what gives? I mean you will always be able to fulfill the inequality for any epsilon.
>Even when trying to PROVE that a limit for a certain series exists, the proof just suddenly stops and q.e.d. Then you just whatever the fuck you want for your inputs and you're done. Circulatory logic at its finest.
I would like to know what OP actually thinks.
I'll be honest with you. Most "advanced" higher level math seems to expand structures of more "basic" concepts in calculus, however, I rarely see how it's any more rigorous or general than the basic structures. Honestly, it's just different and more convoluted notation meaning the same thing.
>I mean you will always be able to fulfill the inequality for any epsilon.
Do you not understand that this is what you're proving?
The whole point of an epsilon-delta proof is to show you can do this. If there's an epsilon it doesn't work for, the number you called the "limit" isn't actually the limit.
Of all the math concepts you will have to learn, this one is probably the most intuitive.
I really don't see the big deal (I'm probably being trolled tho). The definition basically says that, no matter how small a frame you take around the limit, all the terms of the sequence will get in there if you wait long enough.
It's literally what "approaching" means.
I get that it is not easy to work with at the beginning but it really is intuitive
here you go anon
> choosing pi and circle rather than an n-gon
> not defining things carefully in general
> choosing any approximation over an exact value
> suddenly wonder that some things cant be proven
> paradoxes everywhere
> The definition basically says that, no matter how small a frame you take around the limit, all the terms of the sequence will get in there if you wait long enough.
Yeah but then there is the propability to get the exact value of a real number (which is 0), therefore the the chance to get the exact value of a limit is also 0 and you cant construct a frame around something that you cant choose.
Thats like saying x+-1 exist but x doesnt
> N is a set of numbers
> N +( N*-1 ) is a set of numbers called Z
> (N*(N-1))/N is a set of numbers called Q and allow infinitsimals instead of maiking use of a mixed radix
> invent nth sqrt and log and shit
> throw Q in it all over the place
> shit on any order and functional connection
> call it R