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Why doesn't SPP understand that decimal is an imperfect system to represent real numbers? This whole thing has come out of the fact that you can abuse the notation due to its shortcomings.

No matter how we depict real values, they still retain their properties, including the fact there is no next number in the reals. Using decimal's quirky construction to build a theoretical number that comes directly before 1 doesn't change how the numbers actually work. All that's been done is confuse people.

I understand where finitists come from, but this is an extreme form of it, almost to a silly extent. We just have to accept that if one were to have 0.999... written out in its full infinite form, it would equal 1. Just because a task is impossible doesn't mean we can't imagine it.

SPP, if your assumption is that mathematics is limited by our ability to physically compute it, then you fundamentally misunderstand maths. Maths is not about computation, it's about patterns and structures and logical deductions. Through these patterns and structures do we see reflections of reality and use them to create more efficient ways to calculate.

I mean this in no offense, you are the kind of person that would've rejected negative numbers, complex numbers, and the like when they were first proposed. Yet you cannot deny their prevalence in reality and their utility in calculation. Finitism directly opposes the foundation of calculus, yet calculus works exactly as it is supposed to. I can give you a position/time graph from a velocity/time graph through the use of infinitesimals and you cannot deny it's accuracy within the accuracy of the initial measurements.