Cantor wanted to know whether there are sets of numbers which are bigger in size than whole numbers but small enough that they can’t be paired with all infinite decimal expansions. In other words, can there be a tribe whose members are numbered with a set of numbers that beats the whole-number tribe but is outdone by the tribe with all infinite decimal numbers? The name given to the infinity of all infinite decimal numbers is the continuum. The continuum hypothesis posited that there was no infinity smaller than the continuum but larger than the infinity of all whole numbers.
cantor. continuum
