 # Generating Whole Numbers from the Digits 1, 2, 3, 4 and 5

I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the “Law of Frequency of Error.” The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand and marshaled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.

J. R. Newman

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In mathematics, whole numbers are the part of the number system that includes all the positive integers starting from 0. In set theoretic notation, the set of whole numbers is given by W = {0, 1, 2, 3, 4, . . .}.

On other hand, among many mathematical operations, addition (+), subtraction (−), multiplication (×), division (÷), reciprocal (1/x), exponentiation (ax) etc. are well known. Of course, we should not forget fraction (a/b) and decimal (.).

There is a famous mathematics problem in which we are allowed to use only first five natural numbers together with any mathematical operations to generate various whole numbers. In this article, we will show the way to generate whole numbers up to 20 using the digits 1, 2, 3, 4 and 5. But we can generate other whole numbers also. Here, we have considered a few ways to write a particular number, so the list is not exhaustive. If you came across any other way(s) to represent a number, not listed here, please do get back to us.

First we will generate the whole numbers 0, 1 and 2. The list is given below.

Next, is the time for the numbers 3, 4 and 5. The list is given below.

Now we will generate the whole numbers 6, 7 and 8. The list is given below.

We will now generate the whole numbers 9, 10 and 11. The list is given below.

Now is the turn for the numbers 12, 13 and 14. The list is given below.

We will now generate the whole numbers 15, 16 and 17. The list is given below.

Finally, it’s the time to generate the whole numbers 18, 19 and 20. The list is given below.

Of course, we can include other whole numbers in this list. A second blog containing the numbers from 21 to 50 will appear very soon as a continuation to this one.

Your suggestions are eagerly and respectfully welcome! See you soon with a new mathematics blog that you and I call Math1089 – Mathematics for All!“.

1. souravkumarbejgmailcom says:
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