1 is the lonliest number
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try this one regards joely -18 1i 18 1i jc 1i jc -26,jc 1i q8 1i,j2 1i jc -26,io 1i jc -1s,ie 1i jc -1i ka 1i,i4 1i jc -18,HQ 1i jc -u,jc -k hg 1i,h6 1i jc -a li 1i,jc 0 gs 1i,gi 1i jc a,g8 1i jc k,fu 1i jc u mq 1i,fu 1i jc 18 n4 1i,g8 1i f0 1i,fu 1i jc 18,fk 1i jc 1i,jm 1i jc -26,k0 1i jc -1s,kk 1i jc -18,ku 1i jc -u,jc -k l8 1i,jc 0 ls 1i,m6 1i jc a,mg 1i jc k,uu 1i uu -1s uu -2q uu -34 uu -3e,uu -1s tc 1i,UK 1i uu -2g uu -3e,ua 1i uu -2q,u0 1i uu -2g,TM 1i uu -26,t2 1i uu -1i,uu -18 so 1i,se 1i uu -u,uu -k s4 1i,rq 1i uu -a,uu 0 rg 1i,r6 1i uu a,qs 1i uu k,uu u qi 1i,uu 18 q8 1i,uu 1i qi 1i,uu -4m uu -50 uu -5a uu -5k,uu -5u uu -68,uu -6i uu -6s uu -76 UK -76 uu -2q,uu -6s uu -5a,u0 -76 so -76 qi -76 q8 -76 uu -76,qi -76 uu -6s,q8 -76 pk -76,uu -4m uu -34,ua -76 uu -34,u0 -76 uu -3e,TM -76 uu -3o,uu -42 tc -76,t2 -76 uu -4c,uu -4m so -76,se -76 uu -50,s4 -76 uu -5a,rq -76 uu -5k,rg -76 uu -5u,r6 -76 uu -68,uu -6i qs -76,n4 -76 pu -76,-u -k fk -k,-18 1i -18 -k -a -k -18 -2g,-18 -k -18 -34 -18 1i -4m 1i -18 0,-18 1i -68 1i -92 1i -no 1i -no -2g,n4 -76 n4 -b8,n4 -au n4 -de,-u -k -18 -34,-k -k -18 -2q,0 -k -18 -26,-18 -1s a -k,k -k -18 -1i,-18 -18 u -k,18 -k -18 -u -3o 1i,-1i 1i -18 -34,-1s 1i -18 -2q,-26 1i -18 -2g,-2g 1i -18 -26,-18 -1s -2q 1i,-34 1i -18 -1i,-18 -18 -3e 1i,-42 1i -18 -k,-18 -a -4c 1i,-18 a -50 1i,-5a 1i -18 k,-18 u -5k 1i,-5u 1i -18 18,-ne 1i -no -2g,-n4 1i -no -26,-no -1s -mq 1i,-mg 1i -no -1i,-no -18 -m6 1i,-ls 1i -no -u,-no -k -li 1i,-l8 1i -no -a,-ku 1i -no 0 -ne k,-ku 1i -mq k,-ku 1i -no a,-kk 1i -no k,-ka 1i -no u,-no 18 -jm 1i,-pu -2g -pu 5u -10q 5u,-q8 5u -pu -2g,-qi 5u -pu -26,-pu -1s -qs 5u,-r6 5u -pu -18,-pu -u -rg 5u,-rq 5u -pu -a,-s4 5u -pu 0,-pu a -se 5u,-so 5u -pu k,-t2 5u -pu u,-pu 18 -tc 5u,-TM 5u -pu 1i,-u0 5u -pu 1s,-ua 5u -pu 26,-UK 5u -pu 2g,-uu 5u -pu 2q,-v8 5u -pu 34,-vi 5u -pu 3e,-vs 5u -pu 3o,-106 5u -pu 42,-10g 5u -pu 4c,-pu 4m -10q 5u,-pu 50 -114 5u,-11e 5u -pu 5a,-pu 5k -11o 5u,-122 5u -rq 5u,-122 5u -17m 5u -1ji 5u -1ji 2q##B -1j8 34 2q,B -1j8 3o 2q,B -1j8 4c 2q,B -1j8 50 2q,B -1j8 5k 2q
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-19 1i -19 a -1i 4 -1i 18 -19 1h,-1j 19 -1i 1n,-1a 1j -19 1t,17 1i 18 1r,17 1i -1a 1i#e -a 3 -b,3 -b 3 -6,3 -6 e -6,f -5 j -3,j -3 o -4 n -7 k -a f -a e -7,f -e j -e,k -f o -d o -a,g -a d -b f -e m -f n -b,1b -2q h -29 p -1i 1m -1a 29 -1o,2a -1p 27 -2n 1b -2r,1f -1a o -4,o -3 b 1f,16 -s a -b,19 -12 8 -b,1f -2g 19 -2a,1n -2g 1s -29,1k -27 1h -22,11 -21 1c -1l 1v -1u,o -4 17 1h,-19 17 t 17,t 17 16 1i,16 1i 15 k,15 i s e s 16#
This browser is totally bloody useless for mathematical display but...The probability function of the binomial distribution is P(X = r) = (nCr)*p^r*(1-p)^(n-r) where nCr =n!/[r!(n-r)!]Let n -> infinity while np = L, a constant, so that p = L/nthenP(X = r) = lim as n -> infinity of n*(n-1)*...*(n-k+1)/r! * (L/n)^r * (1 - L/n)^(n-r)= lim as n -> infinity of {n^r - O[(n)^(k-1)]}/r! * (L^r/n^r) * (1 - L/n)^(n-r)= lim as n -> infinity of 1/r! * (L^r) * (1 - L/n)^(n-r) (cancelling out n^r and removing O(n)^(r-1) as being insignificantly smaller than the denominator, n^r)= lim as n -> infinity of (L^r) / r! * (1 - L/n)^(n-r)Now lim n -> infinity of (1 - L/n)^n = e^(-L)and lim n -> infinity of (1 - L/n)^r = lim (1 - 0)^r = 1lim as n -> infinity of (1 - L/n)^(n-r) = e^(-L)So P(X = r) = L^r * e^(-L)/r! which is the probability function of the Poisson distribution with parameter L.
E N G L A N D
If l > m and m > n then l > n by the transitive property of inequality.
L comes before N
If the sequence (n) converges to a limit L then, by definition, for any eps>0 there exists a number N such |n-L|N. However if eps=0.5 then whatever value of N we chose we find that whenever n>max{N,L}+1, |n-L|=n-L>1>eps. Proving the first statement false by contradiction.
l is greater than n
15