Question: Invoking algebraic axioms that programmatically work off float approximations

So, basically i plan to define procedures based on if conditions that will assume arbitarily large float approximations as being infinity, as with the example i have uploaded, but i feel that i need some people from here that are smarter than me to tell me why this is going to be terrible or what i need to consider. 

I am willing to consider my current view naive and or inept, however i feel as if computer algebra systems will eventually develop means of reducing the need for floating point results by making concise implicit steps of manipulation on floating point computations, naturally i feel as if these routines are evidence that maybe some of the maple programmers have such an objective, but i do tend to misinterpret everything all the time.



convert(evalf[100](1/RootOf(floor(_Z))), 'rational', 'exact')






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