Are Factorials Always Positive?

Marcus Vance
Marcus Vance
• • 6 min read

The Factorials of Real Negative Integers Have Their Imaginary Part Equal to Zero, Thus Are Real Numbers. Similarly, the Factorials of Imaginary Numbers...

Are Factorials Always Positive?

The factorials of real negative integers have their imaginary part equal to zero, thus are real numbers. Similarly, the factorials of imaginary numbers

imaginary numbers
An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25.
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are complex numbers. The moduli of the complex factorials of real negative numbers, and imaginary numbers are equal to their respective real positive number factorials.

Can factorials be negative?

The factorials for real negative numbers may be defined by the integral equation, MathML. The factorials of negative real numbers are complex numbers. At negative integers the imaginary part of complex factorials is zero, and the factorials for -1, -2, -3, -4 are -1, 2, -6, 24 respectively.

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Are factorial only for positive integers?

n! In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n: = Γ(x + 1), where Γ is the gamma function; this is undefined when x is a negative integer. ...

Marcus Vance

Marcus Vance

Cybersecurity & Digital Privacy Researcher
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Marcus Vance is a cybersecurity auditor and technology writer dedicated to educating the public about online safety, data privacy regulations, enterprise security, and emerging cyber threats.