Saturday, March 13, 2021

Detail #405: Doubly Redundant Numerals

A redundant numeral system is one where numbers have multiple ways of being expressed. This can easily be constructed by, for instance, having digits for larger numbers than the base, e.g. base 10, but digits up to twelve. Let's call them J, K, L (10, 11, 12).

This provides two ways of writing 11: <11>, <B>. 22, likewise, can be written as <22> or <1C>.

A different type of redundancy could be one where some information in the number is given in a redundant fashion. We in fact have some of that already - digit grouping is a redundant feature.

I will use the roman numeral D (500) as an illustration. Imagine we used D for 500, and it permitted the following uses:

D00 = 500
D = 500
D4 = 504
1D = 1500
1D00 = 1500
1500 = 1500

Using the D here would introduce some redundancy: we now know how far away the unit is, even if it is omitted. Imagine further using M as an alternative for 1000. We could also go a slight additive route here, and if we have the letters J K L M N O P Q R S following the previously given pattern, 

DSS would signify 500 + 190 +  19 = 709, which also could be written 709 or 69S or 5SS. The double redundancy, of course, comes from the fact that we can know the D is 500, and that its order of magnitude is not the result of a digit having been lost to the right. 

However, dedicated symbols like these could maybe also permit for things like this:

D250 = 500 + 250 = 750

I will not get into that kind of thing any deeper right now. I am inclined to think I might include something like this in the Bryatesle-Dairwueh number system.

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