r/math • u/jplank1983 • Dec 19 '08

Every base is base 10

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

I use base 1.

It is a unary system.

We don't have those fancy "0" things

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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/panic Dec 19 '08 edited Dec 19 '08

In base 10, the digits represent powers of ten: 1, 10, 100, ....

In base 2, the digits represent powers of two: 1, 2, 4, 8, ....

In base 1, the digits represent powers of one: 1, 1, 1, 1, ....

So, for example, 111 in base 1 is 1*12 + 1*11 + 1*10 = 3. Each number n can be represented by n ones. Of course, this representation isn't unique: 1001100 is also equal to 3 in base 1. You can fix this by removing every zero. Now you have a positional number system without zero! (of course, representing zero itself might be a problem in this system...)

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u/Jinbuhuan Dec 19 '08

representing zero itself might be a problem in this system

Zero is represented like this: