# Zero vs. One: Mathematically Speaking

## Difference between Zero and One

The number zero plays important role in mathematics as an additive identity of real numbers, integers and other algebraic structures. It is denoted by the symbol 0 and it is also called nought, naught in the U.S., nil or “0”. One or 1 – is a unit of counting and is a number that represents a single entity. Anything of unit length has length 1 or one. One is also called Unity.  Photo by garlandcannon Photo by drcorneilus

## As A Number

Zero is neither positive nor negative. It is an integer placed between -1 and 1 on the number line. It is an even number as it is divisible by 2 or two. All integers from zero to infinity are called whole numbers. It quantifies null size. There is no ‘zero’ year in the BC calendar. 1 AD is followed by 1BC. 1 is placed between zero and two on the number line. It is first odd number. 1 is a multiplicative identity and anything multiplied by 1 results in the same thing. Hence one is its own square, cube, factorial and so on.

## In Science

On the Kelvin scale of temperatures, 0 is the coldest possible temperature. On the Celsius scale, 0 is defined as the freezing point of water. In a quantum mechanical system, zero is the lowest possible energy that a system can have.

Zero is of great significance in computer science. It represents the lower bit in a binary system. All data is stored in a computer in the form of binary numbers, right from various fonts of an alphabet to multimedia objects like images, audio or video.

1 is an atomic number of hydrogen. It is used as the higher bit in a binary code. Polyethylene Terephthalate is identified in the Resin Identification Code of recycling as 1.

## In Mathematics

Zero has significance in various branches of mathematics. For example, in the Set Theory it is defined as an empty set. In Propositional Logic it denotes the truth value – False. It is the bottom element of the Lattice in the Lattice Theory. It denotes the initial object of a category in the Category Theory. Zero of function f(x) means the point on the x–axis where the value of this function is zero. Logarithms with base 1 are not defined and 1x is 1 for any value of x. One is neither prime nor a composite. In probability theory one is the probability of an event that will occur definitely.

## Summary

Zero

• It is also called nought, naught (US), nil or “0”.
• Zero is neither positive nor negative.
• There is no ‘zero’ year in the BC calendar.
• On the Kelvin scale of temperatures, 0 is the coldest possible temperature. On Celsius scale 0 is defined as the freezing point of water.
• Zero of function f(x) means the point on x – axis where the value of this function is zero.

One

• 1 (One) – as a unit of counting, is a number that represents a single entity.
• One is its own square, cube, factorial and so on.
• Polyethylene Terephthalate is identified in the Resin Identification Code of recycling as 1.
• One is neither prime nor a composite.
• Logarithms with base 1 are not defined and 1x is 1 for any value of x.

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