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0.9 + 0.09 + 0.009 + .. = 1 Calculations don't add up? 0.9 + 0.09 + 0.009 +.. = 1 is defi ned to mean for every ε > 0 there exists an n such that for every i≥ n we have |(0.9 + ... + 9×10-i) - 1| < ε. Define your calculations to add up. s1 =00000000000... S2 =11111111111... s3 =01010101010... s4 =10101010101... s5 =11010110101... All numbers s6 =00110110110.. s7 =10001000100... we can defi ne s8 =00110011001... s9 =11001100110... S10=11011100101.. S11=11010100100 .. Undefi nable s =10111010011 dark number Add undefi nable dark numbers. Now you're doing math like a mathematician!

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