Difference between revisions of "Axiom of Infinity"
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The '''Axiom of Infinity''' is one of the [[axiom]]s of [[Zermelo-Fraenkel]] set theory. It asserts ([[nonconstructive]]ly) that an [[infinite]] set exists. The [[cardinality]] of this set is usually [[countable]]. | The '''Axiom of Infinity''' is one of the [[axiom]]s of [[Zermelo-Fraenkel]] set theory. It asserts ([[nonconstructive]]ly) that an [[infinite]] set exists. The [[cardinality]] of this set is usually [[countable]]. | ||
| − | Many mathematicians and philosophers take issue with this axiom, asserting that the world and human reasoning are finite in nature--therefore nothing infinite exists. | + | ==Physical Reality of such a set== |
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| + | Many mathematicians and philosophers take issue with this axiom applying to the physical world, asserting that the world and human reasoning are finite in nature--therefore nothing infinite exists. | ||
Christians qualify this statement further by stating that God is infinite, as are all things associated with Him (His Might, His Forgiveness, etc), but our finite minds cannot comprehend them. For this further reason we should not include infinite sets into our mathematical universe. | Christians qualify this statement further by stating that God is infinite, as are all things associated with Him (His Might, His Forgiveness, etc), but our finite minds cannot comprehend them. For this further reason we should not include infinite sets into our mathematical universe. | ||
[[Category:Logic]] | [[Category:Logic]] | ||
Revision as of 01:49, January 5, 2010
The Axiom of Infinity is one of the axioms of Zermelo-Fraenkel set theory. It asserts (nonconstructively) that an infinite set exists. The cardinality of this set is usually countable.
Physical Reality of such a set
Many mathematicians and philosophers take issue with this axiom applying to the physical world, asserting that the world and human reasoning are finite in nature--therefore nothing infinite exists.
Christians qualify this statement further by stating that God is infinite, as are all things associated with Him (His Might, His Forgiveness, etc), but our finite minds cannot comprehend them. For this further reason we should not include infinite sets into our mathematical universe.
