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Equinumerous


Let A and B be two classes of positive integers. Let A(n) be the number of integers in A which are less than or equal to n, and let B(n) be the number of integers in B which are less than or equal to n. Then if

 A(n)∼B(n),

A and B are said to be equinumerous.

The four classes of primes 8k+1, 8k+3, 8k+5, 8k+7 are equinumerous. Similarly, since 8k+1 and 8k+5 are both of the form 4k+1, and 8k+3 and 8k+7 are both of the form 4k+3, 4k+1 and 4k+3 are also equinumerous.


See also

Bertrand's Postulate, Choquet Theory, 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.

Referenced on Wolfram|Alpha

Equinumerous

Cite this as:

Weisstein, Eric W. "Equinumerous." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Equinumerous.html

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