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In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets.
In philosophy and theology, infinity is explored in articles under headings such as the Absolute, God, and Zeno's paradoxes. In Greek philosophy , for example in Anaximander , 'the Boundless' is the origin of all that is.
The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate , [ 1 ] after the lemniscate curves of a similar shape studied in algebraic geometry , [ 2 ] or "lazy eight", in the terminology of livestock branding .
Actual infinity is to be contrasted with potential infinity, in which an endless process (such as "add 1 to the previous number") produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps.
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 ...
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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 ...