The phrase "actual infinity" is correct and usable in written English.
It can be used in discussions related to mathematics, philosophy, or theoretical concepts where the idea of infinity is being examined in a concrete or real sense.
Example: "In set theory, the concept of actual infinity challenges our understanding of numbers and their properties."
Alternatives: "real infinity" or "true infinity".
FitzRalph continues his argument by stating that if there is an actual infinity within bodies, that is to say, if they can actually be divided to infinity, then it is clear that it is possible for God to make an infinite number of other things.
To avoid the use of actual infinity, Eudoxus of Cnidus (c. 400 350 bce) and Archimedes (c.
Since the concept of actual infinity has been crucial to the entire subsequent study of mathematics and physics, this is a particularly important new insight," said Sharp.
However, this question cannot even be formulated mathematically unless infinitely many Xs can be defined on the same sample space, which in turn requires that the underlying experiment involve an actual infinity of coin tosses.
Aristotle influenced subsequent thought for more than a millennium with his rejection of "actual" infinity (spatial, temporal, or numerical), which he distinguished from the "potential" infinity of being able to count without end.
The book's editor Michael Sharp called the discovery, in the treatise The Method of Mechanical Theorems, that at one point Archimedes considers the concept of actual infinity "very important for the history of mathematics and science".
(See also infinity for Aristotle's distinction between actual infinities and potential infinities).
Such actual infinities not only cause philosophical and logical problems, they may also cause problems of a theological nature.
In the first place it assumes that a clear distinction can be drawn between potential and actual infinities, something that was never fully achieved.
Finally, the distinction between potential and actual infinities has played no role in mathematics since Cantor tamed the transfinite numbers certainly the potential infinite has played no role in the modern mathematical solutions discussed here.
In fact, by working seriously with actual infinities Dedekind took a stance incompatible with that of his teacher Gauss, who had allowed for the infinite only as a "manner of speaking" (Ferreirós 1999, ch. 7, earlier Edwards 1983).
