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| Hmmm... What do you mean by '''base doesn't need to be an integer'''? Especially suspicious is the idea to use '''complex''' bases. What numbers are you going to represent in such bases and what are the digits? In my opinion, this part (at least, as written) is rather confusing than revealing... --[[User:Fedja|Fedja]] 19:34, 22 June 2006 (EDT) | | Hmmm... What do you mean by '''base doesn't need to be an integer'''? Especially suspicious is the idea to use '''complex''' bases. What numbers are you going to represent in such bases and what are the digits? In my opinion, this part (at least, as written) is rather confusing than revealing... --[[User:Fedja|Fedja]] 19:34, 22 June 2006 (EDT) |
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− | We can have base <math>i</math>, base <math>\phi</math>, and improper fractional bases like 3/2. In a rational base, any integer may be represented without a decimal point in that base. For complex and irrational bases, we use (I think) 0 or 1 as digits. For a fractional base p/q with max(p,q)=a, we use 0 up to a-1 for digits, i.e. for 3/2, 0,1,2 are digits; for 1/4, we use 0,1,2,3. --[[User:Solafidefarms|solafidefarms]] 21:11, 22 June 2006 (EDT)</math> | + | We can have base <math>i</math>, base <math>\phi</math>, and improper fractional bases like 3/2. In a rational base, any integer may be represented without a decimal point in that base. For complex and irrational bases, we use (I think) 0 or 1 as digits. For a fractional base p/q with max(p,q)=a, we use 0 up to a-1 for digits, i.e. for 3/2, 0,1,2 are digits; for 1/4, we use 0,1,2,3. --[[User:Solafidefarms|solafidefarms]] 21:11, 22 June 2006 (EDT)<math> |
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− | Hmmm..., so how would you represent, say 4 using base 3/2 and digits 0,1, and 2? Also, what would, say, 4 be when written in base <math>i</math> (the latter question is especially interesting, because all possible powers of <math>i</math> are <math>1</math>, <math>i</math>, <math>-1</math>, and <math>-i</math>). Maybe you mean something here but, since even I cannot understand you, there is no hope that 12 year old kids will...--[[User:Fedja|Fedja]] 21:42, 22 June 2006 (EDT) | + | Hmmm..., so how would you represent, say 4 using base 3/2 and digits 0,1, and 2? Also, what would, say, 4 be when written in base </math>i<math> (the latter question is especially interesting, because all possible powers of </math>i<math> are </math>1<math>, </math>i<math>, </math>-1<math>, and </math>-i$). Maybe you mean something here but, since even I cannot understand you, there is no hope that 12 year old kids will...--[[User:Fedja|Fedja]] 21:42, 22 June 2006 (EDT) |
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| First, non-integral bases are not an introductory topic; more of Intermediate or Olympiad. (I have heard it said by several that my work in improper fractional bases is above even that level.) | | First, non-integral bases are not an introductory topic; more of Intermediate or Olympiad. (I have heard it said by several that my work in improper fractional bases is above even that level.) |
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| After closer examination of this article, I decided that the link to [[Improper fractional base]] belongs in the Base Number Topics section. | | After closer examination of this article, I decided that the link to [[Improper fractional base]] belongs in the Base Number Topics section. |
| --[[User:Xantos C. Guin|Xantos C. Guin]] 23:28, 7 August 2006 (EDT) | | --[[User:Xantos C. Guin|Xantos C. Guin]] 23:28, 7 August 2006 (EDT) |
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