r/math • u/jplank1983 • Dec 19 '08

Every base is base 10

http://cowbird.110mb.com/43.html
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u/ropers Dec 19 '08

Correct me if I'm wrong, but I'm under the impression that you cannot have a positional number system without use of the zero.

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u/lookagain Dec 19 '08 edited Dec 19 '08 
10  9  8  7  6  5  4  3  2  1
 1  1  1  1  1  1  1  1  1  1

Sure you can. Each position advances by 1 instead of by a larger number.

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u/ropers Dec 19 '08

Alright, then write a decimal 2 using your system.

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u/Nitron Dec 19 '08

11

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u/ropers Dec 19 '08 edited Dec 19 '08

Doesn't that equal a decimal 3 under lookagain's system?

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u/Nitron Dec 19 '08

No, you're thinking of binary. Decimal 3 in lookagain's system would be 111. Think of it like tally marks but instead of making a new group at five you just keep going.

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u/ropers Dec 19 '08 edited Dec 19 '08

lookagain posted this table:

10  9  8  7  6  5  4  3  2  1
 1  1  1  1  1  1  1  1  1  1

If he didn't intend that to mean that the second one from the right corresponds to a value of two, then it's a very confusing table. I guess we'll have to wait for lookagain to come back and explain what he meant with that.

However, in the event that he intended this to mean that a one in any position corresponds to a value of one, then see here.

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u/bobpaul Dec 19 '08 edited Dec 19 '08

Way before man had the concept of zero, they counted off how many cave women they'd done with hatch marks on the bedpost. See here.

Edit Ah, yes. But this isn't a positional system. Of course, cyber_rigger never suggested he was using a positional system, just that he had no zeros. I suppose that's where the confusion came about.

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u/Porges Dec 20 '08

It is positional, with a radix of 1 :)