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The topological approach is interesting in the sense that it puts minimum requirements on the definition and target sets of the function: You only need to know what subsets are open, you don't even need to know the distance between two elements of a set. If you are interested in real numbers only (or in vector spaces), you can do with the definition (or a simple extension) I gave earlier.
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Why doing it the easy way if it is possible to do it complicated? -
You're not going to be any help to him, then.Originally posted by Ben Kenobi
Well the way I was taught calculus is to understand the fundamental relationship between distance, velocity and acceleration.Comment
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Yes, I ain't much for "pure" math.
Sounds like I was taught the same way he was, the applications first. Engineers tend to see the world that way, and that is how the math was developed in the first place.
It's only later that the theory was developed.Scouse Git (2) La Fayette Adam Smith Solomwi and Loinburger will not be forgotten.
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It's not exactly clear what you mean.Originally posted by Ben Kenobi
Yes, I ain't much for "pure" math.
Sounds like I was taught the same way he was, the applications first. Engineers tend to see the world that way, and that is how the math was developed in the first place.
It's only later that the theory was developed.
What is "the theory" that was developed later than "the math"?
In any case, distance/velocity/acceleration problems were a tiny subset of the intended "applications" of calculus when it was developed.Comment
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