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:: A ( m, n ) = hyper ( 2, m, n + 3 ) − 3.
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:: and m
In modern notation this says that given quantities p, q, r and s, then p: q :: r: s if for any positive integers m and n, np < mq, np = mq, np > mq according as nr < ms, nr = ms, nr > ms respectively.
:: Georges Shoal, in 56-foot ( 17 m ) deep water, 110 miles ( 180 km ) east of Cape Cod 41 ° 44 ′ N 67 ° 47 ′ W / 41. 733 ° N 67. 783 ° W / 41. 733 ;-67. 783 , linked to North Truro, MA.
:: Nantucket Shoals, in 80-foot ( 24 m ) water, 100 miles ( 160 km ) south-east of Rhode Island 40 ° 45 ′ N 69 ° 19 ′ W / 40. 75 ° N 69. 317 ° W / 40. 75 ;-69. 317 , linked to Montauk AFB, Long Island, NY.
:: Un-named Shoal ( Unofficially: Old Shaky ), in 185-foot ( 56 m ) water, 84 miles ( 135 km ) south-east of New York City 39 ° 48 ′ N 72 ° 40 ′ W ( Destroyed, with 28 killed, during a storm on 15 January 1961 ), linked to Highlands, NJ mainland station.
:: 0 → E < sub > 0 </ sub > → E < sub > 1 </ sub > → E < sub > 2 </ sub > → ... → E < sub > m </ sub > → 0
:: and n
:: ( C < sub > 6 </ sub > H < sub > 4 </ sub >)( CO < sub > 2 </ sub > CH < sub > 3 </ sub >)< sub > 2 </ sub > + 2 C < sub > 2 </ sub > H < sub > 4 </ sub >( OH )< sub > 2 </ sub > → 1 / n
:: to show / solve < tt > G </ tt >, show / solve < tt > G < sub > 1 </ sub ></ tt > and … and < tt > G < sub > n </ sub ></ tt >
:: and =
:: 27 < sup > 5 </ sup > + 84 < sup > 5 </ sup > + 110 < sup > 5 </ sup > + 133 < sup > 5 </ sup > =
:: u < sup > 2 </ sup > = 22030 + 28849v − 56158v < sup > 2 </ sup >+ 36941v < sup > 3 </ sup >− 31790v < sup > 4 </ sup >.
:: f ( x ) = a < sub > 0 </ sub > + a < sub > 1 </ sub > x + a < sub > 2 </ sub > x < sup > 2 </ sup >, where a < sub > 2 </ sub > ≠ 0
0.349 seconds.