How did the ancient Greeks use the word apeiron when discussing infinity?

The ancient Greeks used the word apeiron to describe the concept of infinity, carrying connotations of being unbounded, indefinite, undefined, and formless.1

In a cosmological context, the philosopher Anaximander postulated the apeiron as the primal, infinite, and indeterminate ground or origin of all matter, rather than a specific element like water. His philosophy relied on the world’s contrast with this infinite apeiron, from which all things originated and to which they would eventually return.234

In mathematics, while the Greeks found the concept of infinity indispensable for dealing with continuous magnitudes, they generally held an abhorrence for the notion of "actual" infinity. To avoid it, thinkers like Aristotle distinguished between actual infinity and "potential" infinity—the ability to count or divide without end. Consequently, Greek mathematicians developed rigorous logical frameworks, such as the method of exhaustion and the theory of proportions, to reason about infinity as finitely as possible.516