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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 ...
The aleph numbers differ from the infinity commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the ...
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 ...
Eternity, in common parlance, is an infinite amount of time that never ends or the quality, condition or fact of being everlasting or eternal. [1] Classical philosophy , however, defines eternity as what is timeless or exists outside time, whereas sempiternity corresponds to infinite duration.
[1] [3] For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number of integers. [4] 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 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 .
Aristotle, alive for the period 384–322 BCE, is credited with being the root of a field of thought, in his influence of succeeding thinking for a period spanning more than one subsequent millennium, by his rejection of the idea of actual infinity. [7] In Book 3 of his work entitled Physics, Aristotle deals with the concept of infinity in ...
The origins of the cosmological argument can be traced to classical antiquity, rooted in the concept of the prime mover, introduced by Aristotle.In the 6th century, Syriac Christian theologian John Philoponus (c. 490–c. 570) proposed the first known version of the argument based on the impossibility of an infinite temporal regress, postulating that time itself must have had a beginning.