Importance of Zero in Mathematics

The number which constitutes something different from nothing. The digit which builds a number (10, 100, etc.) and can also diminish the value of a number (zero times anything is zero); zero is undoubtedly the most important invention in mathematics. It clears the distinction between positive and negative integers thereby helping to form the number system.

Metaphorically used to indicate a failure, zero as a number isn’t one. In fact, it has its own set of rules. We know Aryabhatta invented it in the mid-fifth century. Unfortunately, we don’t know a lot of important details about zero. So here we present a description of its importance in mathematics, which is way more than just being positional.

History & Evolution

Although Sumerians were the first to develop the counting system, they overlooked a flaw. They didn’t know how to represent the value of a place which had nothing. So, a number like 1025 couldn’t be recorded. But they came up with a plan, which was to use spaces. So the hundredth value in 1025 was left blank. But this gave rise to confusion.

The Babylonians adopted the Sumerian counting system and their solution to the problem were quite effective. They invented a mark which would signify what we later know as zero (although the mark looked nothing like the modern day zero). There was still an issue to be solved and they had no name for the mark.

A few years later Brahmagupta, an Indian was the first to apply zero in arithmetic. He put dots (named ‘shunya’) below the numbers which indicated zero. He had also developed the basic rules like addition and subtraction, but his concept of division by zero was incorrect. Almost four centuries later, Aryabhatta originated the modern decimal-based place value notation. The rules for complex operations of zero were laid by Isaac Newton, G.W. Leibniz, and Rene Descartes.

Utility in Mathematics

  • Mathematically speaking, zero is the number immediately preceding one
  • It’s an even number and neither positive or negative
  • Zero is said to be the cardinality in set theory, denoting emptiness of a set
  • Zeroth-order logic, it is used to denote true or false
  • Algebra, it is considered to be the zero elements, adding important value to the equation
  • Lattice theory, it may signify a bottom element of a bounded lattice
  • Category theory, zero may be used to denote the initial value
  • Recursion theory, zero signifies the Turing degree
  • Various fields of mathematics have zero elements

Fun Facts

  • The name ‘zero’ is derived from the Arabian word ‘sifr’ which also provided the word ‘cipher’
  • It has different names in sports, in football, it’s called ‘nil’, in tennis ‘love’ and in cricket ‘duck’
  • DVDs which can be played in any region are called ‘region 0’
  • The numbers 0 and 1 are not assigned any character in phone dials because they are considered for special purposes
  • Any number, other than zero, raised to the power of 1 is zero.

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