>>12490359Just because I am a finitist does not mean I am an ultrafinitist or a strict constructivist. Therefore, while I know that a fraction with the numbers you have given cannot likely be evaluated (as in the numerator and denominator cannot likely be expressed in base 10 natural numbers with our known computing resources), it does not mean that I believe that such a fraction does not exist.
This is because all of the quantities in your expression are bounded, so the expression you have provided is purely finitary.
While I myself cannot evaluate this expression, I do not need to fall back axiomatics to do assume the ability to construct this object; this is the fundamental difference between the expression you provided and real numbers. I know this object can be constructed just from the natural numbers and some successor operation (however these are defined) in a purely finitary way. On the other hand, to get real numbers, you *need* to make the assumption that an infinite amount of work can be done.
This is not a matter of constructivism; it's a matter of just assuming things you'd like to be true. Just because no one can evaluate expressions involving large natural numbers does not give you the excuse to assume whatever you want and claim you are a non-constructivist.
