# What is an Infinite Word™?

This puzzle is based off the What is a Word™ and What is a Phrase™ series started by JLee and their spin-off What is a Number™ series.

If a word conforms to a certain rule, I call it an Infinite Word™. Use the following examples to find the rule:

$$% set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{1.0}} \def\Title{\textbf{ Infinite }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\ \def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2018.03.05}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{OMISSION}&\text{HYPOCRISY}\\ \hline \text{JEALOUSY}&\text{OBLIVIOUS}\\ \hline \text{OFFSTAGE}&\text{ISOLATION}\\ \hline \text{YAWNER}&\text{EXCITER}\\ \hline \text{SOCIETAL}&\text{MISANTHROPE}\\ \hline \text{FRENZIED}&\text{HOEDOWN}\\ \hline \text{YACHTSWOMEN}&\text{KLEPTOMANIACS}\\ \hline \text{VACUOUS}&\text{PHILOSOPHIC}\\ \hline \text{UNSOCIAL}&\text{SEGREGATION}\\ \hline \text{IMMOLATE}&\text{ZEPPELIN}\\ \hline \text{HEATEDLY}&\text{HEAT}\\ \hline \text{QUESTION}&\text{WEASEL}\\ \hline \text{SEPULCHER}&\text{JAIL}\\ \hline \text{ESCAPISM}&\text{WONDER}\\ \hline \text{MUTATION}&\text{UNIQUE}\\ \hline \text{TRICKERY}&\text{OPINION}\\ \hline \text{VERIFIED}&\text{VALIDATION}\\ \hline \end{array}$$

The puzzle satisfies the series' inbuilt assumption, that each word can be tested for whether it is a Infinite Word™ without relying on the other words.

These are not the only examples of Infinite Words™, many more exist.

CSV version for Analysis:

OMISSION,HYPOCRISY
JEALOUSY,OBLIVIOUS
OFFSTAGE,ISOLATION
YAWNER,EXCITER
SOCIETAL,MISANTHROPE
FRENZIED,HOEDOWN
YACHTSWOMEN,KLEPTOMANIACS
VACUOUS,PHILOSOPHIC
UNSOCIAL,SEGREGATION
IMMOLATE,ZEPPELIN
HEATEDLY,HEAT
QUESTION,WEASEL
SEPULCHER,JAIL
ESCAPISM,WONDER
MUTATION,UNIQUE
TRICKERY,OPINION
VERIFIED,VALIDATION

• It doesn't particularly matter (I assume), but you have two ISOLATIONs in the right-hand column. May 14, 2018 at 15:50
• Oh, and two MISANTHROPEs. May 14, 2018 at 15:50
• @GarethMcCaughan TY, changed them to UNIQUE ones. :) May 14, 2018 at 16:14
• And two WONDERs. May 14, 2018 at 16:15
• An infinite word is one that goes on without end. Consider, for example, the infinite word "banananananananananananananananananananananananan
– Mark
May 15, 2018 at 1:04

An Infinite Word™...

has a single capital letter with a closed region (e.g. A, D, O, P, Q, or R) in its left half and one in its right half, with the center letter of odd-lettered words not being one of those. This bears similarity to an infinity symbol, where there is a closed region on each side (hence the name Infinite Word™, I presume).

There is one undefined condition: it's unclear from the examples above how to consider the letter B, since it has two closed regions. The only word with a B is OBLIVIOUS, which is already disqualified as an Infinite Word™ because it has an O on the right and a OB on the left. If a letter B is treated just like any other letter with a closed region then, for example, BIGOT would be an Infinite Word™.

• Does "OBLIVIOUS" fail because of the "B" then? May 14, 2018 at 19:54
• @AlexisOlson: Yeah. May 14, 2018 at 19:56
• Yes. rot13 (Bqq yrggrerq jbeqf pnaabg unir n "ubyr" va gur zvqqyr yrggre, naq "O" artngrf nal jbeq.) May 14, 2018 at 20:26
• Is it wrong for me to have considered calling this type "A Tainted Word™?" May 14, 2018 at 20:27
• The "undefined condition" noted in the answer, to me at least, is clear. Any B in any position makes two holes—either on the left, the right, or (god forbid!) in the middle—disqualifying the word. May 15, 2018 at 1:41

Infinite words:

have exactly two holes in their all-caps form, like $\infty$ does. Non-infinite words have $0,1$ or $\gt2$ holes.

• except for ZEPPELIN
– JMP
May 14, 2018 at 16:59
• soooooo close... May 14, 2018 at 17:51
• NIPPLE = Infinite word... but NIPPLES is not Infinite May 14, 2018 at 17:56
• @Chowzen Does that mean SUPPLE is infinite but AMPLE is not? =D Specifically because 'gurl erdhver bar ubyr ba rvgure fvqr bs gur jbeq'? May 14, 2018 at 18:24
• @hagfy This is true. May 14, 2018 at 20:29