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I wonder if we could switch to "ation scale" where every number is notated as fractional N-ation required to make it. Then we can fit any natural number we use
by thriftwy 3y ago
I wonder if we could switch to "ation scale" where every number is notated as fractional N-ation required to make it. Then we can fit any natural number we use betwern 3 and 4, and even BB numbers will not be very scary. We get them back to the realm of writedownity.
Is there a function to convert fractional numbers between natural and ation scale? A(2) = 4, A(3) = 27, A(4) = 10 ^ (10 ^ 154), but what's A(3.5)?
- UncombedCoconut 3y agoThis program is at least related to what you want: https://googology.fandom.com/wiki/Hypercalc https://googology.fandom.com/wiki/Hypercalc -- and the community there has devised other systems for representing huge numbers with compact notations.
- srcreigh 3y agoWhat is "fractional N-ation"?
- lifthrasiir 3y agoYou can regard multiplication as repeated additions, exponentiation as repeated multiplications, tetration as repeated exponentiation and so on. Of course they are not just repeated operations; you've got to define them for negative, fractional and complex operands in a justifiable way as well. Note that those operations also form a sequence, so let's rename addition to 1-ation, ..., tetration to 4-ation (in fact tetra- prefix exactly means this) and so on. Now, what could be 2.5-ation or pi-ation?
- thriftwy 3y agoThe point being, what's the pi-ation of pi.