0! should be 0, not 1.
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after 2 votes the winner is...
mdc32
Voting Style:  Open  Point System:  7 Point  
Started:  11/14/2014  Category:  Education  
Updated:  1 year ago  Status:  Post Voting Period  
Viewed:  422 times  Debate No:  65148 
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0 times 0 is equal to 0, so this makes since.
0 factorial is accepted to be one for multiple reasons, which I will outline and briefly explain below. First, let's define factorial. dictionary.com gives us "the product of a given positive integer multiplied by all lesser positive integers." There is no positive integer less than 0, so 0 is not multiplied by anything else, leading to the first reason. Empty Product Pro states that "0 times 0 is equal to 0, so this makes since. [sic]" This is correct, but irrelevant. The additive identity is 0, as for any number n, it is obvious that n + 0 = n. In the same way, 1 is the multiplicative identity. For any number n, n * 1 = n. These identities have been established for a long period of time, and they are commonly accepted by mathematicians. If no numbers are added together (let's think of this as an empty sum), the result is always 0, the additive identity. Similarly, if no numbers are multiplied, the "empty product" is 1, the multiplicative identity. Because 0! has an empty product, the result is 1. The second reason for 0! being 1 deals with factorial and its applications. Empty Set Factorial is commonly used when referring to probability, sets of data, and other similar branches of mathematics. The permutation and combination functions, nPr and nCr respectively, use the factorial function in their equations. One application of factorial itself is the amount of different ways you can arrange a set including n items. This is also a permutation function, namely for any whole number n, nPn. A set of 3 items can be arranged 6 different ways (3!), a set of 4 can be arranged 24 different ways (4!) and a set of 5 things can be arranged 120 different ways (5!). A set with no items in it can only be arranged one way  empty. A third explanation for this situation is purely mathematical, and very logical. Factorial Division 4! and 3! are 24 and 6, respectively. 4 factorial can be represented by 4*(3!), and as a result 4! / 3! is 4. This is reproducible all the way down to 1. 1! / 0! must be 1, and as a result 0! must be 1. Note that this cannot be continued into negative numbers, as the factorial function is only used for positive integers. I look forward to my opponent's response. Thanks for a good debate topic, and hopefully you don't forfeit like many other members of this website. 

BOBISAWESOME forfeited this round.
This website's users are really starting to disappoint me. It either stems from a lack of respect, forgetfulness or something like this, or a lack of confidence in one's answers. If you don't want to post arguments to a debate, don't start it. Vote Con. 
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Vote Placed by lannan13 1 year ago
BOBISAWESOME  mdc32  Tied  

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Reasons for voting decision: Forfeiture
Vote Placed by Enji 1 year ago
BOBISAWESOME  mdc32  Tied  

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Reasons for voting decision: Pro makes no substantial arguments and forfeits. Con's arguments are mathematically correct, and hence win the debate.