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If people use things like exponents and nested factorials can you decide between two numbers without explicitly working out what the number is? It seems like so

If people use things like exponents and nested factorials can you decide between two numbers without explicitly working out what the number is? It seems like sort of a hard programing problem to take the entered text (assuming an unambiguous format - machine parsable) and quickly tell which one is larger. Some numbers that are easy to write down might take years to calculate but if you apply some kind reasoning, similar to algorithm analysis, you might be able to construct arguments for why one number is larger than another.

mjw 16y ago
In general it'd be reducible to the halting problem, if you allowed a Turing-complete language for the number-generating programs. I imagine you could tackle a good subset of the problem though with a symbolic algebra package (mathematica?) if you restricted the form of the number-generating programs to a certain set of mathematical expressions for which it knows enough tactics to reduce the inequalities involved.