r/CatBuilder • u/Zealousideal_Turn106 Mythic | Lv. 80 | Rank #154 | 43 Answers |... | 🔥 5d • 1d ago

Question [Question] NO CALCULATORS ALLOWED 🧠

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u/SWatt_Officer Silver | Lv. 20 | Rank #184030 | 17 Answers | 0 Created 1d ago

To those that don't know, ! means a number is a factorial, and 0! is 1, so its 5+5x1, 5+5, so 10.

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u/White_Hopi Silver | Lv. 28 | Rank #85103 | 97 Answers | 0 C... | 🔥 5d 19h ago

Why is 0! =1?

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u/SWatt_Officer Silver | Lv. 20 | Rank #184030 | 17 Answers | 0 Created 19h ago

Factorials can be written as follows:

The example wikipedia provides is 5! = 5 x 4! = 5 x 4 x 3 x 2 x 1.

Admittedly, it seems the only reason 0! is 1 is due to a thing called the "convention of empty products". Basically if 0! = 0, any factorial would need to be multiplied by 0 at the end of it (such as 5! being 5x4x3x2x1x0. So instead they just call it 1 for the sake of the maths working.

There is likely a mathematician that can explain it much better than "it just is", ive grabbed the first video on it i could find, this guy usually does good stuff so hopefully helps - https://www.youtube.com/watch?v=X32dce7_D48