Explanation on why 0!=1 by hayzeed

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steemstem · @hayzeed · Jun 6 '18

$0.57

Explanation on why 0!=1

<center>![IMG_20180606_184155_756.JPG](https://cdn.steemitimages.com/DQmbTMNg8hDebexpgBEAKTreZKZvxNLC84E81moUe1o6tdT/IMG_20180606_184155_756.JPG)</center>

Yesterday, I posted a tutorial on permutation but I said that I will explain why 0!=1 in my next topic , in case you missed the tutorial click here [Permutation tutorial](https://steemit.com/steemstem/@hayzeed/mathematics-tutorial-on-permutation)

Now let's start.

From my previous post, I stated that factorial notation formula is;
 n! = n * (n - 1) * (n - 2) *..... 3 * 2 * 1

Which will only works when n is greater than 0.

Using the above formula,

6! =  6(6-1)(6-2)(6-3)(6-4)(6-5)

 By simplyfying

6!= 6 * 5 *4 *3 * 2 * 1  ---------------eq(1)
Then
6!= 720 ---------------------------------eq(2)

Let's simplify 5!

5!= 5 * 4 * 3 * 2 * 1  ------------------ eq(3)
5!=120
By substituting 5!= 5 * 4 * 3 *2 *1 in eq(1)

Then we will have,

6! = 6 * 5!

By dividing both side by 6 then,

5! = 6!/6

From eq(2) 6!= 720
Substituting that, we the have

5! = 720/ 6
5!= 120
You can see that we get same answer

Do you get it?

Now we can say that,
4! =5!/5

4!= 120/5

4!= 24

Do you agree with that? If you are still confuse, Let's use the above formula to solve it.

4!= 4(4-1)(4-2)(4-3)
4!= 4 * 3 * 2 * 1
4!= 24 

Hope you aren't confused anymore?

Now, let's proceed

3!= 4!/4
3!= 24/4
3!= 6

2!= 3!/3
2!= 6/3
2!= 2

1!= 2!/2
1!= 2/2
1!= 1

Then,

0!= 1!/1
0!=1/1

0!=1

There are some others ways to explain it but it will be more complicated for beginners because it require using advance mathematics topics.


Follow @hayzeed and visit our blog daily for more tutorial.

## _The picture used in this post was designed by me_

## References
[Numberphile - zero factorial](
https://www.youtube.com/watch?v=Mfk_L4Nx2ZI)
[Math forum - FAQ](http://mathforum.org/dr.math/faq/faq.0factorial.html)

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@minnowsupport · Jun 10 '18

<p>Congratulations!  This post has been upvoted from the communal account, @minnowsupport, by Hayzeed from the Minnow Support Project. It's a witness project run by aggroed, ausbitbank, teamsteem, theprophet0, someguy123, neoxian, followbtcnews, and netuoso. The goal is to help Steemit grow by supporting Minnows.  Please find us at the <a href="https://discord.gg/HYj4yvw"> Peace, Abundance, and Liberty Network (PALnet) Discord Channel</a>.  It's a completely public and open space to all members of the Steemit community who voluntarily choose to be there.</p> <p>If you would like to delegate to the Minnow Support Project you can do so by clicking on the following links: <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=102530.639667%20VESTS">50SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=205303.639667%20VESTS">100SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=514303.639667%20VESTS">250SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=1025303.639667%20VESTS">500SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=2053030.639667%20VESTS">1000SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=10253030.639667%20VESTS">5000SP</a>. <br><strong>Be sure to leave at least 50SP undelegated on your account.</strong></p>

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@procrastilearner · Jun 7 '18

What is this witchcraft?

Kidding aside that's a cool math result, never would have guessed that zero factorial is equal to 1.

👍 hayzeed

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@hayzeed · Jun 7 '18

Lol. Thanks. Math is fun, Always visit my blog for more tutorial.

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@hayzeed · Jun 9 '18

Tutorial on COMBINATION has been posted.

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@steemiansarena · Jun 9 '18

Your post has been upvoted by the @steemiansarena trail. Our goal is to support minnows and help them grow. You can join our discord server [here](https://discord.gg/VXZ4rq) Whastapp [here](https://chat.whatsapp.com/50wJ8HvVsK26pKW4j2HXmS).. You can also support us by either contributing steem or delegating SP to us

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