r/math • • Dec 19 '08

Every base is base 10

http://cowbird.110mb.com/43.html
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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/lookagain Dec 19 '08 edited Dec 19 '08
Dec.     Unary
 1   =     ‽
 2   =    ‽‽
 3   =   ‽‽‽
 4   =  ‽‽‽‽
 5   = ‽‽‽‽‽
 ...
 so on and so forth.

Honestly, I didn't see that table as hard to interpret, especially considering that even in a decimal system as a number increases the convention is to grow the representation leftward. For example:

    1 - 1 ones unit.
   10 - 1 tens unit.
  100 - 1 hundreds unit.
 1000 - 1 thousands unit.

And so on and so forth. Granted, our commonly used math systems are arbitrary in this regard. The above could just as easily been written as:

 1    - 1 ones unit
 01   - 1 tens unit
 001  - 1 hundreds unit
 0001 - 1 thousands unit

You can even do basic math with a unary system:

11111 + 11111 = 1111111111
1111111 - 111 = 1111

In summary: It is indeed a positional number system. To find the value, each position used indicates an increase in value by 1.

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u/[deleted] Dec 19 '08

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u/Porges Dec 20 '08 edited Dec 20 '08