section_path: History/Early Greek
section_name: Early Greek
paragraph_text: Early Greek
  
  The earliest recorded idea of infinity in Greece may be that of Anaximander (c. 610 – c. 546 BC) a pre-Socratic Greek philosopher. He used the word apeiron, which means "unbounded", "indefinite", and perhaps can be translated as "infinite".
  
  Aristotle (350 BC) distinguished potential infinity from actual infinity, which he regarded as impossible due to the various paradoxes it seemed to produce. It has been argued that, in line with this view, the Hellenistic Greeks had a "horror of the infinite" which would, for example, explain why Euclid (c. 300 BC) did not say that there are an infinity of primes but rather "Prime numbers are more than any assigned multitude of prime numbers." It has also been maintained, that, in proving the infinitude of the prime numbers, Euclid "was the first to overcome the horror of the infinite". There is a similar controversy concerning Euclid's parallel postulate, sometimes translated:
  
  If a straight line falling across two straight lines makes internal angles on the same side less than two right angles, then the two straight lines, being produced to infinity, meet on that side that the is less than two right angles.
  
  Other translators, however, prefer the translation "the two straight lines, if produced indefinitely...", thus avoiding the implication that Euclid was comfortable with the notion of infinity. Finally, it has been maintained that a reflection on infinity, far from eliciting a "horror of the infinite", underlay all of early Greek philosophy and that Aristotle's "potential infinity" is an aberration from the general trend of this period.