Definition/Meaning  Word/Phrase 
smallest infinite integer 
alephnought
,
alephnull
,
alephzero

quality of being infinite; without bound or limit 
boundlessness
,
infiniteness
,
infinitude
,
limitlessness
,
unboundedness

approach of an infinite series to a finite limit 
convergence
,
convergency

infinite series that has no limit 
divergence
,
divergency

infinite time 
eternity

(linguistics) a type of grammar that describes syntax in terms of a set of logical rules that can generate all and only the infinite number of grammatical sentences in a language and assigns them all the correct structural description 
generative grammar

metric space that is linear and complete and (usually) infinitedimensional 
Hilbert space

infinite quantity 
infinitude

state of being omniscient; having infinite knowledge 
omniscience

(mathematics) the sum of a finite or infinite sequence of expressions 
series

infinite expanse 
space
