Mathematics is Based on assumptions. it doesn't define what should be and what should not be but it says what would happen if some assumptions are made.

For example, if we took some quantity and gave it a number, "one" for the start, no one will stop us.. you made some assumptions that are valid... similarly if many agree upon you can call the "last number" anything. But Mathematicianss agreed on calling the last finite number "psi" and the last infinnte number "End number"

Now there are sets of numbers that when too close to infinite are so large that they cant serve any propeties that would be useful.. thers is no practical value to use that number.. But you can always assume..