0 - Zero Number

Zero is a number used in mathematics to describe no quantity or null quantity.

When there are 2 apples on the table and we take the 2 apples, we can say that there are zero apples on the table.

The zero number is not positive number and not negative number.

The zero is also a placeholder digit in other numbers (e.g: 40,103, 170).

Zero symbol

The zero number is denoted with the 0 symbol.

The 0 symbol was invented in India.

Math operations with zero

x represents any number.

Operation	Rule	Example
Addition	x + 0 = x	3 + 0 = 3
Subtraction	x - 0 = x	3 - 0 = 3
Multiplication	x × 0 = 0	5 × 0 = 0
Division	0 ÷ x = 0 , when x ≠ 0	0 ÷ 5 = 0
	x ÷ 0  is undefined	5 ÷ 0 is undefined
Exponentiation	0 x = 0	05 = 0
	x 0 = 1	50 = 1
Root	√0 = 0
Logarithm	logb(0) is undefined
Factorial	0! = 1
Sine	sin 0º = 0
Cosine	cos 0º = 1
Tangent	tan 0º = 0
Derivative	0' = 0
Integral	∫ 0 dx = 0 + C

Sets that contain zero

Zero is an element of the natural numbers, integer numbers, real numbers and complex numbers sets:

0 ∈ ℕ₀

0 ∈ ℤ

0 ∈ ℝ

0 ∈ ℂ

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See also

• Factorial
• Logarithm
• Derivative
• Zero number - Wikipedia