The cardinality of set $S$, $|S|$, is the number of unique elements of $S$ if $S$ is a finite set. The cardinality of infinite sets are specially defined quantities such as $\aleph_0$ that are appropriately defined where these infinite sets are defined (see
Local content of this theory
All axioms contained within this theory
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Prove-It Beta Version 0.3, licensed under the GNU Public License by Sandia Corporation.
Presented proofs are not absolutely guaranteed. For assurance, it is important to check the structure
of the statement being proven, independently verify the derivation steps, track dependencies, and ensure that
employed axioms are valid and properly structured. Inconsistencies may exist, unknowingly, in this system.
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under the Quantum Computing Application Teams program. Sandia National Labs is managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a subsidiary of Honeywell International, Inc., for the U.S. Dept. of Energy's NNSA under contract DE-NA0003525. The views expressed above do not necessarily represent the views of the DOE or the U.S. Government.
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