In the unary numeral system, does 1 - 1 = -1 ? Because if this is true, then how would the numbers between 1 and -1 be represented? Where on a number line would .1 and -.1 be? I am not necessarily looking for an answer to each of these other questions; I am curious about the problems that arise if a unary number system allows for negative numbers. Specifically, what is there between 1 and -1? I ask this question because I don't know the answers and I haven't yet found an answer on the Internet.
1 Answers
Here is an answer for the question : " I am curious about the problems that arise if a unary number system allows for negative numbers."
In the unary counting method that I will call "tally stick" counting method (that our ancestors must have practised), one can consider negative numbers in the following way.
You take a point on the stick, and make grooves either on the right (positive quantities) or on the left (negative quantities). Then if you have 7 grooves on the right and 8 on the left, you can consider it as $-1$.
Said in a mathematical way, $-1$ designates the equivalence class of ordered pairs of the form $(n+1,n)$, i.e., $n+1$ tallies on the left, $n$ on the right...
Immediate generalization to any negative number $-a$ represented by the set of ordered pairs $\{(n+a,n) \ | \ n \in \mathbb{N} \}$
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Connected: interesting thoughts about the unary system https://math.stackexchange.com/a/1945471/305862 – Jean Marie Dec 31 '22 at 08:58
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Any comment ?.... – Jean Marie Dec 31 '22 at 13:19