*But which infinity?*The biggest one of course! :-)
Instead of Aleph-0, Aleph-∞
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I just like how WolframMathWorld summed up that whole Aleph-0 craziness:
Renteln and Dundes (2005) give the following humorous mathematical analog of the "99 bottles of beer on the wall" drinking song, which refers to its property that aleph_0-1=aleph_0: "Aleph-null bottles of beer on the wall, Aleph-null bottles of beer, Take one down, and pass it around, Aleph-null bottles of beer on the wall" (repeat).
Incidentally, another variant runs, "99 bottles of beer on the wall, 99 bottles of beer, Take one down, Put it back up, 99 bottles of beer on the wall" (repeat).
Silly, yes, but with that in mind, I chose 0. But an interesting point chacham made:
*Hence, the poll question is really, what is the first representational digit in base 1, colloquially asked as "what is the first number after 0".*
So, once one moves from 0, say addition (after zero) or subtraction (before zero), are they then stuck forever on 1 or -1???
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Comment onRe^2: In base 1, the number after 0 is: