There is also a possibility that physical reality might enjoy an infinite number of dimensions; indeed, quantum mechanics is often formulated in terms of an infinite-dimensional Perhaps the most familiar context for discussing infinity is in metaphysics and theology.

Cantor originated the distinction between the infinities of mathematics, physics, and metaphysics.

Mathematicians are quickly struck by the fact that ordinary intuitions about numbers are misleading when talking about infinite sizes.

To avoid the use of actual infinity, , whereby an area was calculated by halving the measuring unit at successive stages until the remaining area was below some fixed value (the remaining region having been “exhausted”).

The issue of infinitely small numbers led to the discovery of .

He similarly showed that the set of counting numbers and their doubles (i.e., the set of even numbers) could be paired up.

Galileo concluded that “we cannot speak of infinite quantities as being the one greater or less than or equal to another.” Such examples led the German mathematician beginning in 1873.

Alternatively, in the “finite future” view, a cosmic catastrophe at some definite time in the future may destroy the universe: space may collapse to a point, or perhaps a parallel sheet of space (a “brane”) will collide with our universe, annihilating everything.

In any of the catastrophic finite future scenarios, speculation exists that the end of the universe may be followed by the birth of a new universe, in which case the future may in some sense be infinite after all.

The transfinite cardinals include aleph-null (the size of the set of whole numbers), aleph-one (the next larger infinity), and the continuum (the size of real numbers).

These three numbers are also written as ℵ showed that ZFC cannot prove CH.

If matter were to be infinitely divisible, then each object would in principle contain a potentially infinite collection of particles.

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