一道微积分的讨论题，求大神回答，最好是英文回答 10
InthePreviewofCalculusatthestartofourtextbook,wewereintroducedtoZenoofElea,the5thcent...
In the Preview of Calculus at the start of our textbook, we were introduced to Zeno of Elea, the 5th century BC philosopher as well as his paradoxes. Recall that Zeno claimed it must be impossible to ever reach a wall, since you must first walk half the distance to the wall, then half this distance, and half that distance, and so-on. Since it would take an infinite number of halvings, Zeno reasoned, it would take an infinite amount of time to ever reach the wall.
While such thought experiments sometimes seem irrelevant to "real life", there are several real physical situations that mirror the issues surrounding Zeno's paradoxes. Take for example, the radioactive decay of Carbon-14. A naturally occurring isotope of Carbon, 14C has a half-life of 5,730 years. This means that after every 5,730 years, about half of the 14C atoms in a sample will decay into an isotope of Nitrogen, 14N. If you wait another 5,730 years the number of 14C atoms will halve again.
This is very similar to Zeno's paradox and raises some interesting questions.
1. We all know that you will easily reach the wall in Zeno's paradox, but it is less clear whether all of the 14 C isotopes in a sample will eventually decay. What, if anything, is different between these two situations?
2. If you started with, say, one billion 14 C atoms, will it ever be the case that they all decay to 12 C? If so, how long would it take?
3. What if you started with just one 14 C atom. What do you think happens then?
To earn full credit for this discussion, you must post a total of at least three entries over at least two days. Of course, more is welcome and encouraged. You are welcome to focus your discussion on whichever topic interests you most, or spread your wisdom throughout all three topics. 展开
While such thought experiments sometimes seem irrelevant to "real life", there are several real physical situations that mirror the issues surrounding Zeno's paradoxes. Take for example, the radioactive decay of Carbon-14. A naturally occurring isotope of Carbon, 14C has a half-life of 5,730 years. This means that after every 5,730 years, about half of the 14C atoms in a sample will decay into an isotope of Nitrogen, 14N. If you wait another 5,730 years the number of 14C atoms will halve again.
This is very similar to Zeno's paradox and raises some interesting questions.
1. We all know that you will easily reach the wall in Zeno's paradox, but it is less clear whether all of the 14 C isotopes in a sample will eventually decay. What, if anything, is different between these two situations?
2. If you started with, say, one billion 14 C atoms, will it ever be the case that they all decay to 12 C? If so, how long would it take?
3. What if you started with just one 14 C atom. What do you think happens then?
To earn full credit for this discussion, you must post a total of at least three entries over at least two days. Of course, more is welcome and encouraged. You are welcome to focus your discussion on whichever topic interests you most, or spread your wisdom throughout all three topics. 展开
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