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In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1.
Yet Cantor was still able to pair each such fraction to a whole number 1 - 1 / 1; 2 - 2 / 1; 3 - 1 / 2... etc. through to ∞; i.e. the infinities of both fractions and whole numbers were shown to have the same size. But when the set of all infinite decimal numbers was considered, Cantor was able to prove that this produced a bigger infinity.
This is a list of articles about prime numbers.A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers.
Below are the primetime rankers for broadcast, cable and premium cable networks in 2024, among total viewers (as well as the top 50 list in adults 18-49).
DeMarvion Overshown's season is over. His availability for 2025 is in doubt. The rising Dallas Cowboys star suffered tears to the ACL, MCL and PCL in his right knee during Monday's loss to the ...
a 0 = 1, a 1 = 2, a 2 = 4, a 3 = 8,... The sequence of forward differences is then Δa 0 = a 1 − a 0 = 2 − 1 = 1, Δa 1 = a 2 − a 1 = 4 − 2 = 2, Δa 2 = a 3 − a 2 = 8 − 4 = 4, Δa 3 = a 4 − a 3 = 16 − 8 = 8,... which is just the same sequence. Hence the iterated forward difference sequences all start with Δ n a 0 = 1 for every ...
From January 2008 to April 2011, if you bought shares in companies when E. C. “Pete” Aldridge, Jr. joined the board, and sold them when he left, you would have a -25.3 percent return on your investment, compared to a -7.3 percent return from the S&P 500.
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