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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.
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 .
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.
Infinity means a never-ending sequence of numbers trailing off into, well, infinity. But that also necessitates that there’s technically an infinite number of infinities forming a hierarchy of ...
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 absolute infinite (symbol: Ω), in context often called "absolute", is an extension of the idea of infinity proposed by mathematician Georg Cantor.It can be thought of as a number that is bigger than any other conceivable or inconceivable quantity, either finite or transfinite.
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 ...
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