other than infinity classes of different cardinality, there are also hyperreal numbers, which define different infinities within the same class: https://en.wiki

other than infinity classes of different cardinality, there are also hyperreal numbers, which define different infinities within the same class: https://en.wikipedia.org/wiki/Hyperreal_number https://en.wikipedia.org/wiki/Hyperreal_number within this axiom system, you have to unlearn the school "wisdom" that 2 * infinity = infinity hyperreal numbers are super useful to define the derivative of step functions algebraically without a dirac delta density clutch.