Single Digit Representations of Natural Numbers

 

Intro

Inder J. Taneja established symmetric representation of numbers where one can use any of 9 digits giving the same number. The representations of natural numbers from 0 to 1000 are given using only single digit in all the nine cases, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9. This is done only using basic operations: addition, subtraction, multiplication, potentiation, division.

Overview

Let “a” be a single digit positive natural numbers, i.e. a, belongs to {1, 2, 3, 4, 5, 6, 7, 8, 9}. The easiest way to represent the number by single digit is:

0 = a − a;
1=a/a;
2=(a+a)/a;
3=(a+a+a)/a;
4=(a+a+a+a)/a;
5=(a+a+a+a+a)/a …

We can see that as number increases, we need to use more digits to write it. But it is not true, for example we can get 10 as 10=11-1=2*2*2*2+2. In this case we used only 3 digits for 1 and 4 digits for 2.

The main aim of this work is to write natural numbers from 0 to 1000 in terms of each digits 1, 2, 3, 4, 5, 6, 7, 8 and 9, with “as less as possible digits”, using only the basic operations:
/*author mentioned only 4 basic operations, namely addition, subtraction, multiplication and division; however in his work we can see the usage of concatenation*\

Here is the link to download the full PDF version of Inder J. Taneja’s work. Enjoy the reading!

There will be more articles about Taneja’s work. Feel free to give any comments 🙂

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  1. Interesting! I am looking forward to reading your other articles))

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