apeir-, apeiro- +

(Greek: boundless, infinite)

1. The indeterminate and indefinite ground, matter, or first principle of all being postulated by Anaximander.
2. Anaximander's Greek word for the boundless extent of the universe as undifferentiated matter.

Although Plato made only scant reference to this notion of what is unlimited, the neoplatonic philosophy of Plotinus elevated it as the material principle of all change.

Anaximander (611-547 B.C.), of Miletus, was a presocratic Greek philosopher and student of Thales who believed the universal substance to be infinity rather than something resembling ordinary objects.

Anaximander derived the world from a nonperceptible substance called the apeiron, "unlimited". This state preceded the "separation" into contrasting qualities; such as, hot and cold, wet and dry, and therefore represents the primitive unity of all phenomena.

Anaximander subscribed to the philosophical view that unity could definitely be found behind all multiplicity.

apeirophobia (s) (noun) (no plural)
An excessive fear of infinity or something that has no end: Individuals who have apeirophobia like to have terms defined and distances measured, and appreciate the accurate predictability of things in their lives.