# Dating direct infinity

Although Plato thought of the ) on have supposed the Absolute to be infinite.What is meant by “the Absolute” depends, of course, upon the philosopher in question; it might be taken to mean God, an overarching universal mind, or simply the class of all possible thoughts. Some view this as evidence that the Absolute is infinite.

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when one asks if there are infinitely many stars or if the universe will last forever.

Using a so-called “diagonal argument,” Cantor showed that the size of the counting numbers is strictly less than the size of the real numbers. Unlike a finite set, an infinite set can have the same cardinality as a proper subset of itself.

Cantor used a diagonal argument to show that the cardinality of any set must be less than the cardinality of its power set—i.e., the set that contains all the given set’s possible subsets. Cantor called the sizes of his infinite sets “transfinite cardinals.” His arguments showed that there are transfinite cardinals of endlessly many different sizes (such as the cardinals of the set of counting numbers and the set of real numbers).

In a metaphysical discussion of God or the Absolute, there are questions of whether an ultimate entity must be infinite and whether lesser things could be infinite as well.) and his followers initially believed that any aspect of the world could be expressed by an arrangement involving just the whole numbers (0, 1, 2, 3,…), but they were surprised to discover that the diagonal and the side of a square are ) shared the general Greek abhorrence of the notion of infinity.

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 main reason is simply that the status of physical infinities is quite undecided.

In physics one might look for infinities in space, time, divisibility, or dimensionality.

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