Importance of Zero's in Mathematics
Ten Interesting Facts About Zero
- Zero was invented by Brahmagupta(Hindu astronomer and mathematician) in 628 AD in India , used later by the Persians and Arabs and later in Europe.
- 0 (zero) is both a number and the numerical digit used to represent that number in numerals.
- The zero number is denoted with the 0 symbol.
- Zero is unbiased, which means there is no such thing as -0 and +0
- 1/0=∞ and 1/-0=-∞ are wrong in terms of strict math. So the mathematicians call it UNDEFINED.
1) Zero Addition
Addition of a number plus zero is equal to the number
n + 0 = n
Example
1 + 0 = 1
2) Zero Subtraction
Subtraction of a number minus zero is equal to the number
n - 0 = n
Example
1 - 0 = 1
3) Zero Multiplication
Multiplication of a number times zero is equal to zero
n x 0 = 0
Example
1 x 0 = 0
4) Zero Division
Division of a zero by a number is zero
0 ÷ n = 0
Example
0 ÷ 1 = 0
5) Zero Power
The power of a number raised by zero is one
n0 = 1
Example
10 = 1
6) Square root of Zero
The square root of 0 is also 0
This is because 0 multiplied or divided by any number is 0.
7) Is Zero Odd or Even number
The set of even numbers is:
{... ,-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, ...}
The set of odd numbers is:
{... ,-9, -7, -5, -3, -1, 1, 3, 5, 7, 9, ...}
Zero is an integer multiple of 2:
0 × 2 = 0
Zero is a member of the even numbers set:
0 ∈ {2k, k∈ℤ}
Therefore, zero is an even number and not an odd number.
8) What Type of Number is Zero
Zero is a real number, integer , Rational and whole number that is neither positive or negative.
The set of integer numbers:
ℤ = {0,1,2,3,4,5,6,7,8,...}
Zero is a member of the set of integer numbers:
0 ∈ ℤ
Therefore, Zero is an integer number.
A rational number is a number that can be expressed as the quotient of 2 integer numbers
ℚ ={n/m; n,m∈ℤ}
Zero can be written as a quotient of two integer numbers.
For example:
0 = 0/3
Therefore, Zero is a rational number.
9) Zero Number Facts Table
| Operation | Rule | Example |
|---|---|---|
| Addition | n + 0 = n | 5 + 0 = 5 |
| Subtraction | n - 0 = n | 5 - 0 = 5 |
| Multiplication | n × 0 = 0 | 5 × 0 = 0 |
| Division | 0 ÷ n = 0, when n ≠ 0 | 0 ÷ 5 = 0 |
| x ÷ 0 is undefined | 5 ÷ 0 is undefined | |
| Exponentiation | 0n= 0 | 05= 0 |
| n0= 1 | 50 =1 | |
| Root | √0 =0 | √0 =0 |
| Logarithm | logb(0) is undefined | undefined |
| Factorial | 0! = 1 | 0! = 1 |
| Sine | sin 0º = 0 | sin 0º = 0 |
| Cosine | cos 0º = 1 | cos 0º = 1 |
| Tangent | tan 0º = 0 | tan 0º = 0 |
10) Math without Zero
Today, its difficult to imagine how you could have mathematics without zero.
Without the concept of zero as a number, none of this would be possible.
See Also