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But what's the point? If we already know how to find the limit, why must we go through a process of ingenuity algebra to tell ourselves, "okay it works and it only took us [insert a very long time]"

Are there people who are

*that*skeptical? Yes I realize the math was created before computers, but what's the point of having it now? If you seriously need a theorem with fancy words and symbols to confirm that your limit is right, doesn't that mean you are just unsure of what you are doing?

I mean I finally understood how to use Epsilon definition (and it's true meaning thanks Mark44), but it looks like I am just computing limits backwards with this method