六十年代初,美国数理逻辑学家罗宾逊指出,实数并没有把直线填满,实数还可以扩充为超实数。极限、微分、积分都可以重新加以解释,并以新的装束出现。这当然是一大新闻。由此形成的一门学科,就是“非标准分析”。不少人誉之为“明天的微积分”,评价甚高,这里介绍它的大意。 In the early 1960s, the American mathematical logician Robinson pointed out that real numbers do not fill up straight lines, and real numbers can also be expanded to super real numbers. Limits, differentials, and integrals can all be reinterpreted and appear in new costumes. This is certainly a big news. The resulting discipline is “non-standard analysis.” Many people hailed it as “Tomorrow’s Calculus,” and the evaluation is very high. Here is what it says.