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In the philosophy of mathematics, the abstraction of actual infinity, also called completed infinity, [1] involves infinite entities as given, actual and completed objects. The concept of actual infinity has been introduced in mathematics near the end of the 19th century by Georg Cantor , with his theory of infinite sets , later formalized into ...
Cantor said: The actual infinite was distinguished by three relations: first, as it is realized in the supreme perfection, in the completely independent, extra worldly existence, in Deo, where I call it absolute infinite or simply absolute; second to the extent that it is represented in the dependent, creatural world; third as it can be conceived in abstracto in thought as a mathematical ...
Are numbers and mathematical concepts real or invented? What is the nature of time—does it exist independently of perception? Is infinity real, or is it a mental construct?
The term goes back to Leibniz's theory of possible worlds, [2] used to analyse necessity, possibility, and similar modal notions.In short, the actual world is regarded as merely one among an infinite set of logically possible worlds, some "nearer" to the actual world and some more remote.
The relevant section of Two New Sciences is excerpted below: [2]. Simplicio: Here a difficulty presents itself which appears to me insoluble.Since it is clear that we may have one line greater than another, each containing an infinite number of points, we are forced to admit that, within one and the same class, we may have something greater than infinity, because the infinity of points in the ...
Google aims to release commercial quantum computing applications within five years, Google's head of quantum told Reuters on Wednesday, in a challenge to Nvidia's predictions of a 20-year wait.
Microsoft unveiled Majorana 1, a quantum chip the company says is powered by a new state of matter. The new chip allows for more stable, scalable, and simplified quantum computing, the company says.
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 is eternal and infinite, or boundless (apeiron), subject to neither old age nor decay, which perpetually yields fresh materials from which everything we ...