The Instigator
BOB-IS-AWESOME
Pro (for)
Losing
0 Points
The Contender
mdc32
Con (against)
Winning
8 Points

0! should be 0, not 1.

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Post Voting Period
The voting period for this debate has ended.
after 2 votes the winner is...
mdc32
Voting Style: Open Point System: 7 Point
Started: 11/14/2014 Category: Education
Updated: 2 years ago Status: Post Voting Period
Viewed: 476 times Debate No: 65148
Debate Rounds (2)
Comments (0)
Votes (2)

 

BOB-IS-AWESOME

Pro

0 times 0 is equal to 0, so this makes since.
mdc32

Con

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.
Debate Round No. 1
BOB-IS-AWESOME

Pro

BOB-IS-AWESOME forfeited this round.
mdc32

Con

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.
Debate Round No. 2
No comments have been posted on this debate.
2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by lannan13 2 years ago
lannan13
BOB-IS-AWESOMEmdc32Tied
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Total points awarded:04 
Reasons for voting decision: Forfeiture
Vote Placed by Enji 2 years ago
Enji
BOB-IS-AWESOMEmdc32Tied
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Total points awarded:04 
Reasons for voting decision: Pro makes no substantial arguments and forfeits. Con's arguments are mathematically correct, and hence win the debate.