Georg Cantor Quote

In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand through a definition. However, this domain cannot itself be something variable, since otherwise each fixed support for the study would collapse. Thus this domain is a definite, actually infinite set of values. Hence each potential infinite, if it is rigorously applicable mathematically, presupposes an actual infinite.


"Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" ["Over the different views with regard to the actual infinite numbers"] - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886)

Picture Quote 1

In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand...

Picture Quote 2

In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand...

Picture Quote 3

In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand...

Picture Quote 4

In order for there to be a variable quantity in some mathematical study, the domain of its variability must strictly speaking be known beforehand...