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A problem with a septimal system.

  1. Jul 27, 2014 #1
    I'm reading a textbook of mathematics 'What is mathematics?' and I've got a problem with septimal system.

    Symbol 10416 in the septimal system denote 2610 (decimal system).

    [itex] 1*7^4+0*7^3+4*7^2+1*7+6 = 2610 [/itex]

    But I can't understand why 7416 in the septimal system denote 2610 too.

    [itex] 7*7^3+4*7^2+1*7+6 = 2610 [/itex]

    Where is my mistake?
     
  2. jcsd
  3. Jul 27, 2014 #2

    Orodruin

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    In base N you only use numbers 0 to N-1.

    Examples:
    Binary (base 2): 0 and 1
    Decimal (base 10): 0 to 9
    etc
     
  4. Jul 27, 2014 #3

    ehild

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    The digit "7" does not exist in the septimal system.

    ehild
     
  5. Jul 27, 2014 #4
    Ok. I see. In the septimal system a base is 7 i.e. 0 to 6. I thought 1 to 7. It was my mistake.

    Thanks for your answers.
     
  6. Jul 27, 2014 #5

    SteamKing

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    Also, 7*7^3 = 7^4, whatever system you are using.
     
  7. Jul 28, 2014 #6
    Thank you.
     
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