Let and
be two classes of positive
integers. Let
be the number of integers in
which are less than or equal to
, and let
be the number of integers in
which are less than or equal to
. Then if
and
are said to be equinumerous.
The four classes of primes ,
,
,
are equinumerous. Similarly, since
and
are both of the form
, and
and
are both of the form
,
and
are also equinumerous.
See also
Bertrand's Postulate, Prime Counting Function
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References
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 21-22 and 31-32, 1993.
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Cite this as:
Weisstein, Eric W. "Equinumerous." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Equinumerous.html