Importance of Number 1

                    Important Characteristics of 1

The Greek did not consider 1 as a number. German Kobel in 1537 wrote in his book on computation –wherefrom thou understandest that 1 is no number, but it is a generatrix, beginning, and foundation for all other numbers. The Greek considered that 1 was both even and odd because when 1 is added to even number it produces odd and vice versa. 2 is an even number but 2 + 1 = 3 is an odd. On the other hand 3 is odd and 3+ 1 = 4 is even. Let us see some features of one.

1.      In the real number system, 1 can be represented in two ways as a recurring decimal.          

   0.9999… = 1            and 1.000 =1

2.      If a ZERO means nothing, number ONE is the opposite. Everybody wants to grab number position in the world in their respective fields.           

3.      It is one of the first non- zero Natural number. A natural number is a counting number that begins with 1 and goes to infinity. It is denoted by N. Hence, N = {1 , 2, 3, 4, ….) is a set of natural number.

4.      It is the first odd number. A number which is written in the form of 2n + 1 is called an odd number. In simple word, a number which is not divisible by 2 is called an odd number. For example – 1, 3, 5, 7, 9, …

5.      It is the only number other than 0(ZERO) whose square is the same as itself.                 

        0² = 0 and 1² = 1

6.      The root of modern 1 traces back to Indian Devnagri numeral.

             

7.      A , B, C, D, E, M, T, U, V, W,Y have one line of symmetry. The line of symmetry is a line which divides the Pictures into two parts and they form a mirror image of the other, that is the images in the both the side of the line are reflection of other, when it folded one side over the another along the line of symmetry are equal.

8.      A Mobius strip has one (1) edge and one (1) surface. The Mobius strip has the mathematical property of being non –orientable. It can be realized as a ruled surface. It was discovered by German mathematicians August Ferdinand Mobius and Johann Benedict Listing in 1858.

  

9.      One can’t be used as the base of a positional numeral system.

10.  The logarithm base 1 is undefined.

11.   One (1) is neither prime nor composite number. A prime number has two factors 1 and the number itself whereas a composite number has more than 2 factors.

12.  Factorial of zero (0) is one, i.e. 0! = 1.

13.  One (1) is called the multiplicative or reflexive identity of multiplication. If you multiply any number say a by 1 you will get no change in the result obtained. In simple word, a x 1 = a.

14.  One can be partitioned in one way.

15.   In the Peano axiom, 1 is the successor of 0.

16.  One is the first figurative number of every kind, such as Triangular number, Pentagonal number and Centered Hexagonal number.

17.  One is the magnitude of a unit vector. ǀ ˆi ǀ = ǀ jˆ ǀ = ǀ kˆ ǀ = 1

18.   Probability of an event that is almost certain is 1 (one) i.e. P (A) = 1. Such event is called Sure event.

19.  Number 1 , 11 , 111 , 1111 are all triangular numbers in the base – 9.

           Read More on Number on my book The Power of Mathematical Numbers published by Prabhat Prakashan and available on website for sale.

            Rajesh Kumar Thakur

r     rkthakur1974@gmail.com