Zero (0)
Zero represents nothing, an empty value. How long it took to develop a symbol for zero depends on what you consider, but it still took quite a while for such an important concept. The ancient Egyptian hieroglyph "nfr", 𓄤, was used in records to represent when no food was gained or lost in trades, but it doesn't exactly mean zero. One of, if not the very first, recordings of a symbol for zero is the Hellenistic zero, a small circle, around 140 BCE. It is sort of a point of no return, 0*n for any n is 0 and n^0 is 1 (except 0), and prone to unsolvable forms, like a/0, 0^0, and log(0) in any given base.
Infinitesimal (ε)
Infinitesimal is specifically defined as the smallest positive real number which is not zero. The "dx" used commonly in calculus is of infinitesimal length, and infinitesimal has use in the surreal and hyperreal numbers where it is denoted as ε.
Let's just get all the huge reciprocals out of the way...
1/Croutonillion
1/Utter Oblivion
1/Oblivion
1/Hollom's Number (I_a(200)^-1)
1/Large Number Garden Number ((f^10(10{10}10)^-1)
1/BIG FOOT (FOOT^10(10^100)^-1)
1/Rayo's Number (Rayo(10^100)^-1)
1/Σ(1919)
1/Loader's Number (D^5(99)^-1)
1/Meameamealokkapoowa (({L100,10}_10,10)^-1)
1/Tritar (Tar(3)^-1)
BITG (BIGG^-1)
Smallest named googolism larger than zero, using intended value, since it is ill-defined.
1/THE HUS (S(U(H(3)))^-1)
1/SCG(13)
1/Golapulus (({10,10(100)2}&10)^-1)
1/TREE[3]
1/Lineatrix ((10&10&10)^-1)
1/Blasphemorgulus ((E100{#,#,1,2}100)^-1)
1/Godsgodulus ((E100#{#}#100)^-1)
1/Kungulus ((X^^^100&10)^-1)
1/Pentacthulum ((E100#^^^#100)^-1)
1/Goppatoth ((10^^100&10)^-1)
1/Tethrathoth ((E100#^^#100)^-1)
1/Gongulus ({10,10(100)2}^-1)
Bowers mentions this number in his 'Another Reality' page. 'The odds of this is approximately one out of a gongulus!' (The event shown in the comic is probably not actually as rare as 1/gongulus.)
1/Xappol ({10,10(2)2}^-1)
Okojo-Ermine Number (~{54,55(1)2}^-1)
Was known as the smallest googolism for a good while until BITG was added to the wiki in 2023. Note that it is the smallest currently well-defined googolism. Also, it is not a reciprocal (technically it is but you get the point), but it is placed in the Reciprocal Realm because it is in the range of most other googological reciprocals.
1/Iteral ({10,10(1)2}^-1)
1/BOX_M~ ((M_((M_1)+1))^-1)
1/Supertet ({4,4,4,4}^-1)
1/Graham's Number ((G_64)^-1)
Because if someone else mentioned it, I will. Will anyone even get that?
1/Boogol ({10,10,100}^-1)
1/Tritri ({3,3,3}^-1)
1/Giggol ({10,100,2}^-1)
Now, we have reached the section where most reciprocals are gone.
~10^-360,783
This is approximately the chance that a being which types at random will generate the entirety of Shakespeare's Hamlet perfectly. I nickname this the Monkey Number because said being is commonly referred to as a number.
~10^-183,800
Ditto but without correct punctuation, capitalization, or spaces being required.
1/(52!) (~1.2*10^-68)
The chance of shuffling a 52-card deck in any specific order. Its reciprocal, 52!, is quite infamous as an example of the extent of probability.
Googolminex (10^-(10^100))
This number was named in the Book of Numbers by Conway and Guy. A silly little pun. Plex, plus, drop the -us and add the -ex, similarly, minex, minus shares the same rule.
Googol-minutia (10^-100)
Surprisingly exists within the realm of the universe. The ratio of the volume of the smallest particles to the volume of the observable universe is around a googol-minutia.