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If a fixed fraction x of a given amount of money P is lost, and then the same fraction x of the remaining amount is gained, the result is less than the original and equal to ...

The nth-order Sierpiński carpet graph is the connectivity graph of black squares in the nth iteration of the Sierpiński carpet fractal. The first three iterations are shown ...

A sigma-compact topological space is a topological space that is the union of countably many compact subsets.

A family composed of countably many discrete families.

A family composed of countably many locally finite families.

The signed deviation is defined by Deltau_i=(u_i-u^_), so the average deviation is Deltau^_=u_i-u^_^_=u_i^_-u^_=0.

A test for determining the probability that a given result could not have occurred by chance (its significance).

The 6-polyiamond illustrated above.

sum_(n=1)^(infty)1/(phi(n)sigma_1(n)) = product_(p prime)(1+sum_(k=1)^(infty)1/(p^(2k)-p^(k-1))) (1) = 1.786576459... (2) (OEIS A093827), where phi(n) is the totient function ...

Let f(1)=1, and let f(n) be the number of occurrences of n in a nondecreasing sequence of integers. then the first few values of f(n) are 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, ... ...