Ripheus23

https://www.wolframalpha.com/ can be used to check some of my statements about transfinite arithmetic. For example, inputting "aleph 0 ^ aleph 0 ^ aleph 0" yields the same answers as "(aleph 0 ^ aleph 0) ^ (aleph 0 ^ aleph 0)" (but note that if you don't use the parentheses like that, you get a different answer) and also "beth 1 ^ beth 1" yields the same answers as the three-step staircase (thus indirectly verifying that c ^^ 2 = aleph-0 ^^ 3). Now there's no way I know of to use up-arrow notation in Wolfram Alpha, so conversions would have to be manual (conversions for checking, that is), but I think the basic information proofs are still helpful.