Studying Mathematics Thread

[GrandizerII]

That's amazing I've probably seen it before but I've forgotten it if so. The integral function makes more intuitive sense, I think, when viewed as a "summing" of a continuous series. This is shown here by the discrete summing function becoming an integral as the intervals between the terms tends to zero.

It's again hilarious to imagine getting an exact answer any other way. Draw the graph, then get a piece of string...

Of course, you could use a computer program to get more and more exact approximations. But it's astonishing to me how you can cut right through that to get an exact answer very quickly, assuming you can complete the integral of course! Otherwise, you're back to approximate methods anyway.

It's amazing to me how useful the limit has been as a concept in deriving formulas for certain variables that otherwise would've probably been impossible to attain without it. Despite everything I've posted here, I'm still at the very beginning of the journey of maths, and only recently have I started to realize just how amazing some of these theorems and concepts and tools really are.