Math Tips & Tricks (Playlist): • Math Tips & Tricks
Why 0 Factorial is always 1? 😲 Math Tips & Tricks
Why 0 Factorial is always 1 explanation with examples by Prabhat ranjan for class 12, boards, IIT JEE 2025, JEE Main 2025, JEE Advanced 2025, IIT JEE 2026, JEE Main 2026, JEE Advanced 2026.
"Why 0 Factorial is Always 1? Math Tips & Tricks" by Prabhat Ranjan offers a clear and comprehensive explanation of why the factorial of 0 is defined as 1, an important concept in Class 12 Mathematics and essential for competitive exams like IIT JEE 2025, JEE Main 2025, and JEE Advanced 2025, as well as their equivalents in 2026. The factorial function, denoted as n!, is the product of all positive integers up to n, but 0! is defined as 1 for consistency in mathematical formulas and combinatorial logic. From a combinatorial perspective, 0! represents the number of ways to arrange zero objects, which is exactly one way: doing nothing. Mathematically, this definition ensures formulas for permutations and combinations work correctly even when n is 0. Additionally, using the recursive definition of the factorial function, n! = n × (n-1)!, we find that to maintain consistency, 1! = 1 × 0!, implying 0! must be 1. Furthermore, the Gamma function, which extends the factorial to non-integer values, requires that Γ(1) = 0! equals 1 to satisfy its integral definition. Prabhat Ranjan's detailed explanation, supported by practical examples and proofs, helps students understand why 0 factorial is set to 1, reinforcing their grasp of foundational mathematical principles critical for academic and competitive success.
All these aspects have been covered by Prabhat Ranjan in full detail in his new KZread video.
I am Prabhat Ranjan, currently pursuing B.Tech in Mechanical Engineering from NIT Jamshedpur.
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