If I give you one of each letter in the alphabet what's the largest you can spell (in word form)?
Bonus: What's the smallest?
Bonus 2: What if you can use the words "minus", "plus" and "times"?
Answer
For a number immensely bigger than ω, consider the uncountably infinite number hidden below. (Note, by the way, that ω is countably infinite, and rather than being the biggest something, it is in fact “the smallest infinite ordinal ... as it is the least upper bound of the natural numbers” [1]). So omega is a good candidate for the first bonus, the smallest number one can spell if given one of each letter in the alphabet.
Answer:
The transfinite number aleph sixtyfour appears to be the biggest aleph (ℵ) number one can spell if given one of each letter in the alphabet.
Note that ℵ64>ℵ63>...ℵ1=2ℵ0>ℵ0=ω.
(For a big number that doesn't quite work because it has two a's and e's, see wikipedia's Aleph-ω article; aleph omega is the least upper bound of ℵn:n∈{0,1,2,…}. But if we use five Roman and one Greek letter, or one Hebrew and one Greek letter, aleph ω or ℵω work ok.)
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