The Power of 5 Fives in Generating Whole Numbers

There are three ruling ideas, three so to say, spheres of thought, which pervade the whole body of mathematical science, to someone or other of which, or to two or all three of them combined, every mathematical truth admits of being referred; these are the three cardinal notions, of Number, Space and Order. Arithmetic has for its object the properties of numbers in the abstract. In algebra, viewed as a science of operations, the order is the predominating idea. The business of geometry is with the evolution of the properties of space, or of bodies viewed as existing in space.


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Whole numbers include the natural numbers and zero (0). Basic mathematical operations include addition (+), subtraction (), multiplication (×), division (÷), exponentiation (ax), square root (), cube root, etc. Advanced operations include the use of trigonometric and inverse trigonometric, logarithmic, exponential, factorial, etc. functions.

There is a famous mathematics problem in which we are allowed to use 5 fives and one or more mathematical operations to generate various whole numbers. In this blog post, we will show you how to generate whole numbers up to 15 using 5 fives. The problem is commonly known as 5 fives problem and is well known.

Here, we have considered only a few ways to represent a particular number, so the list is not exhaustive. If you wish to include any other representation not included in this list, please do get back to us through comments. Moreover, a second part will appear as a continuation of this blog post, where numbers from 16 to 50 will be considered.

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

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