Algebraic reasoning is independent of the number system used. If you are reasoning about utility functions in the abstract and if your reasoning does not make use of any properties of numbers, then it doesn’t matter what numbers you use. You’re not using any properties of finite numbers to define anything, so the fact of whether or not these numbers are finite is irrelevant.
Algebraic reasoning is independent of the number system used. If you are reasoning about utility functions in the abstract and if your reasoning does not make use of any properties of numbers, then it doesn’t matter what numbers you use. You’re not using any properties of finite numbers to define anything, so the fact of whether or not these numbers are finite is irrelevant.