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整数、有理数、实数都有无穷多个。哪个更“多”?这个问题困扰着相当多的人。笔者在以前的文章里说过,整数、有理数都是无穷多个,从包含的角度看,整数集是有理数集的子集,但因为可以建立元素间的一一对应,因此可以通俗地说:它们一样“多”。而且,尽管都是无穷多个元素,但它们都可以排成一列,并可以一个一个地数出来,因此它们都是可数的。(要知道,不是所有由无穷多个元素组成的集合的元素都可以排成一列,并一个一个数出来的,如介于0到1之间所有实数构成的集合,就没有办法将它的元素排成一列,并一个一个数出来)
Integers, rational numbers, real numbers have an infinite number. Which one is more “more ” This problem bothers a considerable number of people. The author said in previous articles that integers and rational numbers are an infinite number. From the point of view of inclusion, integer sets are a subset of rational numbers, but because one-to-one correspondence between elements can be established, They are the same “more ”. And although they are an infinite number of elements, they all line up and count one by one, so they are all countable. (Be aware that not all elements of a collection of infinitely many elements can be aligned and counted one by one, such as a collection of all real numbers between 0 and 1, there is no way to have its elements Lined up and counted one by one)