These words refer to great quantities or to things extending without end in space, time or number. Infinite is the most general here. Spatially, it refers to something that has no boundary: in a theory that space is infinite . It may be a less precise substitute for eternal: a kind of immortality that results if matter is finite and space infinite . It may refer strictly to quantity, as in mathematics, in which case it refers to a quantity that always exceeds any other. Theologically, it refers to something absolute or perfect: God’s infinite mercy. Often the word is used hyperbolically for any great amount, or simply as a superlative: an infinite bore.

The remaining words are primarily restricted to infinite quantities or size, but all may refer to things whose boundaries have not yet been discovered or cannot be formulated. In addition to these possibilities, boundless can specifically point to something that is unconstricted or unconstrictable: his boundless optimism. The word often refers hyperbolically to any great amount: the country’s boundless natural resources. Limitless suggests a situation in which no end is in sight or in which there is as much of something as could be used or desired: a limitless supply of drinking water; an artist’s limitless freedom to depict nature as he sees it in terms of form and colour. Illimitable is more formal than the previous words and suggests, in addition to its shared meanings, something to which no boundary can practicably be set.

• Every source of energy in the universe theoretically emits waves that travel an illimitable distance.

The word may also suggest infinite extension in one dimension: defining a line as having illimitable length but no width.