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*\

1. 