When is two plus two not equal to four?

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• Very good answer! Base 3 for example can not have a 4 within its digits! Very good answer!

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  by slothmister on November 4th, 2007

• no sweat! that's what I am here for!

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  by Audiotron on November 4th, 2007

• ONLY in the Base 3 and Base 4 number systems, because they have a numerical digit "2", but not a "4", and then it is a 'false representation', of sorts (a false logic 'game'), because there is no numeric digit-value for "4", but the resulting value is, of course, in reality, equal to "4", none-the-less. (Base 2 does not have a numeric digit "2", and Base 5 and up have a numeric digit "4") Counting to 10 in various number systems:
  
  Base 2: 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010 (binary)
  Base 3: 0, 1, 2, 10, 11, 12, 20, 21, 22, 30, 31 (2 + 2 = 11)
  Base 4: 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22 (2 + 2 = 10)
  Base 5: 0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20
  Base 8: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12 (octal)
  Base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (decimal)
  Base 16: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A (, B, C, D, E, F, 10) (hexadecimal)
  
  For Base b, the largest numerical digit used in that system is b -1, and the numerical representation for the number b is always "10". (add 1, roll around to zero, and carry the one -- Binary: 1 + 1 = 10; Octal: 7 + 1 = 10; Decimal 9 + 1 = 10; Hexadecimal: F + 1 = 10; etc...)

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  by BeeDee314 on November 17th, 2010