Apeiron

Apeiron (ἄπειρον) is a Greek word meaning "(that which is) unlimited," "boundless", "infinite", or "indefinite" from ἀ- a-, "without" and πεῖραρ peirar, "end, limit", "boundary", the Ionic Greek form of πέρας peras, "end, limit, boundary"

The apeiron is central to the cosmological theory created by Anaximander, a 6th-century BC pre-Socratic Greek philosopher whose work is mostly lost. From the few existing fragments, we learn that he believed the beginning or ultimate reality (arche) is eternal and infinite, or boundless (apeiron), subject to neither old age nor decay, which perpetually yields fresh materials from which everything we can perceive is derived. Apeiron generated the opposites, hot-cold, wet-dry etc., which acted on the creation of the world. Everything is generated from apeiron and then it is destroyed by going back to apeiron, according to necessity. He believed that infinite worlds are generated from apeiron and then they are destroyed there again.

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Apeiron Brittanica

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Hippasus

Hippasus of Metapontum (5th century BC), was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this. However, the few ancient sources which describe this story either do not mention Hippasus by name (e.g. Pappus) or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Some modern scholars though have suggested that he discovered the irrationality of √2, which is believed to have been discovered around the time that he lived.

Ancient Roman Cement

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Diogenes and Alexander

Thereupon many statesmen and philosophers came to Alexander with their congratulations, and he expected that Diogenes of Sinope also, who was tarrying in Corinth, would do likewise. But since that philosopher took not the slightest notice of Alexander, and continued to enjoy his leisure in the suburb Craneion, Alexander went in person to see him; and he found him lying in the sun. Diogenes raised himself up a little when he saw so many people coming towards him, and fixed his eyes upon Alexander. And when that monarch addressed him with greetings, and asked if he wanted anything, "Yes," said Diogenes, "stand a little out of my sun." It is said that Alexander was so struck by this, and admired so much the haughtiness and grandeur of the man who had nothing but scorn for him, that he said to his followers, who were laughing and jesting about the philosopher as they went away, "But truly, if I were not Alexander, I would be Diogenes."

Diogenes and Alexander

Diogenes