Georg Cantor Quote

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly dissimilar to, and I might even say in principle the same as, my method described above of introducing transfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.


As quoted in Understanding the Infinite (1994) by Shaughan Lavine


The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite...

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite...

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite...

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite...