What would base 11 be?

Base 10 uses these digits: {0,1,2,3,4,5,6,7,8,9}; base 2 uses: {0,1}; but what would base 1 be?


Let’s say we define Base 1 to use: {0}.
Because 102 is equal to 0102, would all numbers be equal?

The way I have thought Base 1 might be represented is tally marks, 010 would be represented by nothing. So, 5 in Base 1 would be represented by 00000? Or we could define Base 1 to use: {|} and 5 would be |||||?

Answer

You’re exactly right that such a system would be represented by the use of arbitrary tally marks. Such a system is known as a Unary Numeral System (Wikipedia Entry):

The unary numeral system is the bijective base-1 numeral system. It is the simplest numeral system to represent natural numbers: in order to represent a number N, an arbitrarily chosen symbol representing 1 is repeated N times. This system is used in tallying. For example, using the tally mark |, the number 6 is represented as ||||||.

There is no explicit symbol representing zero in unary as there is in other traditional bases, so unary is a bijective numeration system with a single digit. If there were a ‘zero’ symbol, unary would effectively be a binary system. [boldface mine] In a true unary system there is no way to explicitly represent none of something, though simply making no marks represents it implicitly. Even in advanced tallying systems like Roman numerals, there is no zero character; instead the Latin word for “nothing,” nullae, is used.

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Source : Link , Question Author : Justin , Answer Author : amWhy

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