Factorials? What are They? A Simple Kind of Mathematics Shorthand

What are factorials? A variable is a symbol, often written as a letter of the alphabet that stands for a number that can vary in value. For example, take your age. That varies every year, doesn’t it? This year your age may be, say 21. If so, in 365 days your age will be 22. Another 365 days after that and your age will be 23.

Thus age is a function of time. For you, we can write right now:

A = 21

If the number of years that pass equals n, then for next year, n = 1 and

A_n = 21 + n

So,

A₀ = 21 + 0 = 21
A₁ = 21 + 1 = 22
A₂ = 21 + 2 = 23
A₃ = 21 + 3 = 24

and so on.

What Are Factorials?

Now there is nothing special about the letter A. It can be replaced by any other symbol the reader may choose. So let’s choose a new variable symbol, F. We choose to follow this symbol with, of all things, an exclamation point (!). We define this symbol to mean the mathematics operation factorial. What is a factorial?

Written F! it means a product of the form

F(F‒1)(F‒2)(F‒3)… until we reach the value 1.Thus, if F = 7,

F! = 7(7‒1)(7‒2)(7‒3)(7‒4)(7‒5)(7‒6) = 7(6)(5)(4)(3)(2)(1) = 5040

It’s Your Turn!

Problem: Solve these factorials: F = 3, F = 5, F = 11. Write out the steps.

[Answers] 6; 120; 39,916,800

If you were unable to solve the above problems, you may wish to watch this YouTube video on the topic. While there are other videos on the topic at that site, some of them have been made needlessly complex. It is better to learn a topic, than to be impressed by and kept ignorant of the topic.

Note: You might also enjoy Mathematical Powers – A Simple Insight

References:

• WolframMathWorld: Factorial

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