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Math as a whole literally is not real, it's a made up language game that humans use.
The idea that math with the real numbers or infinities is more or less real than some finitist math, is equivalent to saying the rules of the game of chess is more or less real than the rules of the game of Go. It's retarded. They are both just made up rules. They have no connection to anything other than themselves, because they're both just human languages based on human undefined notions and human axioms.
IF you want to use ZFC do it, if you want to drop choice or LEM go ahead, if you want to say only things that are computable in finite space/time are valid go ahead. None of you are more or less correct or valid from each other because platonism isn't real and you're all retarded schizos.
