# Zero Factorial

**URL:** <https://boards.straightdope.com/t/zero-factorial/17560>\
**Category:** Great Debates\
**Created:** [March 1, 2000, 4:53am UTC](https://boards.straightdope.com/t/zero-factorial/17560 "2000-03-01T04:53:00Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![jeturgeon](https://avatars.discourse-cdn.com/v4/letter/j/74df32/32.png) [@jeturgeon](https://boards.straightdope.com/u/jeturgeon)\
**Post date:** [March 1, 2000, 4:53am UTC](https://boards.straightdope.com/t/zero-factorial/17560/1 "2000-03-01T04:53:00Z")

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Can someone pleeeease explain this for me. Throughout all of my math classes, mostly Algebra, I was always told that zero factorial (0!) is equal to 1. Now I understand how 3! is the same as 6, and 5! is the same as 120, and so forth, but I cannot figure out the 0! mystery. Any help would be appreciated.

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**Author:** ![Nu\_Vo\_Da\_Da](https://avatars.discourse-cdn.com/v4/letter/n/97f17d/32.png) [@Nu\_Vo\_Da\_Da](https://boards.straightdope.com/u/Nu_Vo_Da_Da)\
**Post date:** [March 1, 2000, 4:57am UTC](https://boards.straightdope.com/t/zero-factorial/17560/2 "2000-03-01T04:57:00Z")

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Don’t you think this should be in GQ?  
(and sorry, can’t really help you with the math there)

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**Author:** ![Bored2001](https://avatars.discourse-cdn.com/v4/letter/b/e47774/32.png) [@Bored2001](https://boards.straightdope.com/u/Bored2001)\
**Post date:** [March 1, 2000, 4:59am UTC](https://boards.straightdope.com/t/zero-factorial/17560/3 "2000-03-01T04:59:00Z")

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Well, I really have no clue, but I’ve learned something about math. If it doens’t follow the rule then…theres a special rule!! or it is by definition :D. 0!=1 is probably the latter.

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**Author:** ![Gaudere](https://avatars.discourse-cdn.com/v4/letter/g/e495f1/32.png) [@Gaudere](https://boards.straightdope.com/u/Gaudere)\
**Post date:** [March 1, 2000, 5:20am UTC](https://boards.straightdope.com/t/zero-factorial/17560/4 "2000-03-01T05:20:00Z")

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[Moderator Hat ON]

Yeah, I think this should go to the mathematically-inclined in General Questions. Here ya go, Manny, Nickrz…

[Moderator Hat OFF]

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**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\
**Post date:** [March 1, 2000, 5:21am UTC](https://boards.straightdope.com/t/zero-factorial/17560/5 "2000-03-01T05:21:00Z")

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The most natural way is to think of it as an “empty product”. n! is defined to be the product of all positive integers less than or equal to n. That’s an empty set when n=0, so you’re multiplying over an empty product (there’s nothing left to be multiplied). Empty products are generally defined to be equal to 1, because that’s the multiplicative identity (the multiplicative “nothingness”, I guess you could say). Similarly, empty sums are generally defined to be 0, since that’s the additive identity.