| 1. | This idempotent ultrafilter enables us to find an appropriate infinite set .
这个幂等的超滤子能使我们找到一个适当的无限集。 |
| 2. | Countably infinite set
可数无限集合 |
| 3. | And that this corrected equation is itself only an imperfect a roximation to an infinite set of quantum field - theoretical equatio
而这个得以纠正的方程式就其本身而言也只是一个不完美的近似值，趋近于无穷无尽的一整套量子场论方程式。 |
| 4. | And that this corrected equation is itself only an imperfect approximation to an infinite set of quantum field - theoretical equations
而这个得以纠正的方程式就其本身而言也只是一个不完美的近似值，趋近于无穷无尽的一整套量子场论方程式。 |
| 5. | One of the wonders about language and language use is that with a finite set of rules speakers can produce and understand an infinite set of sentences
语言与语言使用的奇妙处之一在于，说话者可以运用一组数量有限的规则来表达和理解数量无限的句子。 |
| 6. | 3 one of the wonders about language and language use is that with a finite set of rules speakers can produce and understand an infinite set if sentences
3语言与语言使用的奇妙处之一在于，说话者可以运用一组数量有限的规则来表达和理解数量无限的句子。 |
| 7. | It is proposed that no qualitative difference can be established between word ? formation rules and syntactic rules , since both types are capable of generating infinite sets of linguistic forms , both are recursive , and neither is subject to limitations on the length of the derivatives
但这并不表明两者有质的差别，因为构词规则和句法规则一样，有生成无限集合的可能，有递归性，理论上没有长度上的限制。 |
| 8. | In particular , some properties of the solution set of the equation a 0 x = b ( where " 0 " denotes sup - inf composition ) are given when the domain is an infinite set on lattice [ 0 , 1 ] . prom the coefficients of the equation aqx = 6 , it is showed that a sufficient and necessary condition that the solution set is nonempty and one for existence of an attainable solution or an unattainable solution
特别在[ 0 ， 1 ]格上对无限论域方程a ? x = n (其中“ ? ”表示sup - inf合成)的解集的性质作了讨论，仅从方程的系数出发给出了方程解集非空的充要条件以及存在可达解或不可达解的充要条件。 |
| 9. | Thus ， for instance ， it may come as a shock to mathematicians to learn that the schrodinger equation for the hydrogen atom is not a literally correct description of this atom ， but only an approximation to a somewhat more correct equation taking account of spin ， magnetic dipole ， and relativistic effects ； and that this corrected equation is itself only an imperfect approximation to an infinite set of quantum field - theoretical equations
因此，举例来说，对数学家而言，了解到下述情形可能会令其惊愕不已，即薛定谔( schrodinger )的氢原子方程式并非是对该原子作出的一种绝然正确的描述，而仅仅是个近似值，趋近于一个在某种程度上更为正确的将自旋、磁性偶极子、以及相对论效应考虑在内的方程式；而这个得以纠正的方程式就其本身而言也只是一个不完美的近似值，趋近于无穷无尽的一整套量子场论方程式。 |
