teaching:topics:calculus:sequences
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teaching:topics:calculus:sequences [2021/01/13 13:47] simon |
teaching:topics:calculus:sequences [2022/07/26 13:43] (current) simon |
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| Can we possibly get a sensible, finite, answer when we try to add up an infinite number of positive numbers all greater than zero? | Can we possibly get a sensible, finite, answer when we try to add up an infinite number of positive numbers all greater than zero? | ||
| - | This is a very ancient problem in mathematics ... and the different ways of resolving (or banishing) it have been profoundly important to mathematics, physics and wider ideas of philosophy. | + | This is a very ancient problem in mathematics --- the different ways of resolving (or banishing) it have been profoundly important to mathematics, physics and wider ideas of philosophy. And to the history of the development of modern science, technology and industry along with modern economies and societies. |
| == == | == == | ||
| <wrap #paradox>Consider a simple question like this:</wrap> | <wrap #paradox>Consider a simple question like this:</wrap> | ||
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| the 'second derivative' of position with respect to time, and the positions and masses involved. This is quite a big leap. | the 'second derivative' of position with respect to time, and the positions and masses involved. This is quite a big leap. | ||
| Quite a lot of our school curriculum is learning about the mathematics they developed in that time. | Quite a lot of our school curriculum is learning about the mathematics they developed in that time. | ||
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| They were laying the foundations of classical mechanics and the science on which we have built modern technology, industry and society. We have dug much deeper since, and found the universe actually behaves in very weird and wonderful ways indeed. Today's mathematicians and scientists are still spending their lives exploring and explaining it, there are still questions to be answered as challenging now as these questions were then. | They were laying the foundations of classical mechanics and the science on which we have built modern technology, industry and society. We have dug much deeper since, and found the universe actually behaves in very weird and wonderful ways indeed. Today's mathematicians and scientists are still spending their lives exploring and explaining it, there are still questions to be answered as challenging now as these questions were then. | ||
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