Why 1 = 0!

To all of those of you who lie awake at night wondering about the factorial function...

1 = 0!

Why?

Because of the following:

n! can be defined as (n-1)! * n =n!

which can be expressed as n! * (n+1) = (n+1)!

which, through dividing both sides of the equation by (n+1) becomes n! = (n+1)!/(n+1)

Thus, when we plug in n when n = 0, we get

0! = (0+1)!/(0+1)

and, since 1! is equal to 1, we get

0! = 1/1 = 1

NOTE: the factorial function n! is primarily defined as the multiplication of all numbers from 1 to n.

blog it? :|C_BozkurT_C

I believe that this is a highly important piece of mathematical awesomeness that needs to be discussed, even if the discussion consists primarily of "lolwut?" ;)

NOTE: the factorial function n! is primarily defined as the multiplication of all numbers from 1 to n.

thepwninator

[QUOTE="thepwninator"]

NOTE: the factorial function n! is primarily defined as the multiplication of all numbers from 1 to n.

VacantPsalm

Not all math is done in the javascript math expressions ;)

In fact, most logicians actually use the '~' to indicate "not"

I think this formula is important in creating a real-life Hulk because it enraged the **** out of me. As some green food dye and steroids to the mix and we got it.

Go go Gadget Bruce Banner mutation! *Flies away on go go gadget helicopter*

I have absolutely no idea what you just said.

And here I was expecting to see a proof for 1 = 0, not 1 = 0!. :P

I like the whole 0.999... = 1 mind****, too.

And here I was expecting to see a proof for 1 = 0, not 1 = 0!. :P

I like the whole 0.999... = 1 mind****, too.

GabuEx

Also I noticed that too (1=0!), though I don't entirely know if that means his claim of 1=0 is wrong or not.

Well, the universe is still intact, better check your math on that one.metroidfood

Believe me-I did. My math professor today was incapable of discerning why euler's number (defined as the sum for all n's greater than or equal to zero of 1/n!) was 2.7-ish rather than 1.7-ish, so I told him about the above mathemagics, which he did not believe. He called me out on it and told me to come to the front of the cIass and show the (presumed to be flawed) logic used on the blackboard so he could show why it was wrong.

He found no flaws in my logic :)

Also I noticed that too (1=0!), though I don't entirely know if that means his claim of 1=0 is wrong or not.

DigitalExile

1 does not equal 0, but it does equal 0! (0 factorial).

n^2 - n does not equal n. Fail.MindFreeze

It does for n = 0 :|

Not all math is done in the javascript math expressions ;)

In fact, most logicians actually use the '~' to indicate "not"

thepwninator

Screw up on the second lineWhicker89

Nope. All mathemagics here are correct :)

Or, at least, as far as my professor and I can tell :)

[QUOTE="Whicker89"]Screw up on the second linethepwninator

Nope. All mathemagics here are correct :)

Or, at least, as far as my professor and I can tell :)

Yeah, the math is sound. There are numerous reasons for why 0! is considered to be 1; another more intuitive reason is that it's the number of ways that you can put 0 items in order.

[QUOTE="thepwninator"]

[QUOTE="Whicker89"]Screw up on the second lineGabuEx

Nope. All mathemagics here are correct :)

Or, at least, as far as my professor and I can tell :)

Yeah, the math is sound. There are numerous reasons for why 0! is considered to be 1; another more intuitive reason is that it's the number of ways that you can put 0 items in order.

I have never actually been in a statistics course, so I was unaware of the fact that it was also an indication of the number of ways you could put n items in order. The only use I was familiar with for it was the definition of euler's number :)

I have never actually been in a statistics course, so I was unaware of the fact that it was also an indication of the number of ways you could put n items in order. The only use I was familiar with for it was the definition of euler's number :)

thepwninator

Yeah, that's even the original definition of n!, if I recall correctly. Basically, if you need to put n items in order, you have n choices of locations for the first item, then (n - 1) choices for the second, and so on.

Hey, does anyone know the 1 = 2 formula? I know how it fails but I'd still like to see it for the lulz. I find the thought of everyone being totally wrong veeeery pleasing for some reason.VacantPsalm

Yup, the "proof" of that goes like this:

a = b

a^2 = ab

a^2 - b^2 = ab - b^2

(a + b) (a - b) = b (a - b)

a + b = b

a + a = a

2a = a

2 = 1

This is like 9th grade math all over again. Damn teacher pulling brackets and letters from nowhere! I thought this was math! When did the alphabnet come into play? *Runs off crying*DigitalExile

2 + 2 = 4

All better?

[QUOTE="thepwninator"]

I have never actually been in a statistics course, so I was unaware of the fact that it was also an indication of the number of ways you could put n items in order. The only use I was familiar with for it was the definition of euler's number :)

GabuEx

Yeah, that's even the original definition of n!, if I recall correctly. Basically, if you need to put n items in order, you have n choices of locations for the first item, then (n - 1) choices for the second, and so on.

Hey, does anyone know the 1 = 2 formula? I know how it fails but I'd still like to see it for the lulz. I find the thought of everyone being totally wrong veeeery pleasing for some reason.VacantPsalm

Yup, the "proof" of that goes like this:

a = b

a^2 = ab

a^2 - b^2 = ab - b^2

(a + b) (a - b) = b (a - b)

a + b = b

a + a = a

2a = a

2 = 1

For those who can't figure it out completely because not everyone is math orientated, just substitue "1" for every A and B.

Ya, that math is definitely flawed and it's simple to figure out where. At the bolded section. If A=B, then B=A so anywhere we see B we can substitue A, and then the equation looks like this, A + A = A, so we know that is where the "proof" phails a 10 the scale of EPIC PHAIL!

For those who can't figure it out completely because not everyone is math orientated, just substitue "1" for every A and B.

Bluestorm-Kalas

Well, that's not really the flawed portion; that's just an indication that something somewhere has gone awry. The actual problem is in the transition between

(a + b) (a - b) = b (a - b)

and

a + b = b

because to get to the second line from the first you'd have to divide by 0.

[QUOTE="DigitalExile"]This is like 9th grade math all over again. Damn teacher pulling brackets and letters from nowhere! I thought this was math! When did the alphabnet come into play? *Runs off crying*GabuEx

2 + 2 = 4

All better?

I thought it was 22 :?

[QUOTE="DigitalExile"]This is like 9th grade math all over again. Damn teacher pulling brackets and letters from nowhere! I thought this was math! When did the alphabnet come into play? *Runs off crying*GabuEx

2 + 2 = 4

All better?

Ok, now listen to this one. If you wanna do a percentage of something, say successful times you hit a duck with a stone, If you haven't tried yet, your denominator is 0, and since you haven't tried yet either so is you're numerator. Now your percentage is the numerator divided by the denominator times one hundred. So:

0/0=*head explodes!*

[QUOTE="Bluestorm-Kalas"]

Ya, that math is definitely flawed and it's simple to figure out where. At the bolded section. If A=B, then B=A so anywhere we see B we can substitue A, and then the equation looks like this, A + A = A, so we know that is where the "proof" phails a 10 the scale of EPIC PHAIL!

For those who can't figure it out completely because not everyone is math orientated, just substitue "1" for every A and B.

GabuEx

GabuEx, let's team up and find the max value of y=tanx. I think we can do it! :P

[QUOTE="DigitalExile"]This is like 9th grade math all over again. Damn teacher pulling brackets and letters from nowhere! I thought this was math! When did the alphabnet come into play? *Runs off crying*GabuEx

2 + 2 = 4

All better?

I was going to ask a question but I got an HTML error, now I don't care.

[QUOTE="GabuEx"]

[QUOTE="DigitalExile"]This is like 9th grade math all over again. Damn teacher pulling brackets and letters from nowhere! I thought this was math! When did the alphabnet come into play? *Runs off crying*I_pWnzz_YoU

2 + 2 = 4

All better?

I thought it was 22 :?

I have won the game.

GabuEx, let's team up and find the max value of y=tanx. I think we can do it! :P

Bluestorm-Kalas

Infinity.

There, that was easy. :P

[QUOTE="I_pWnzz_YoU"][QUOTE="GabuEx"]

[QUOTE="DigitalExile"]This is like 9th grade math all over again. Damn teacher pulling brackets and letters from nowhere! I thought this was math! When did the alphabnet come into play? *Runs off crying*Bluestorm-Kalas

2 + 2 = 4

All better?

I thought it was 22 :?

No, 6+9=69

[QUOTE="Bluestorm-Kalas"]

GabuEx, let's team up and find the max value of y=tanx. I think we can do it! :P

GabuEx

Infinity.

There, that was easy. :P

Actually (I don't exactly know how America works) but I'm taking my math C30 class right now, and I'm finding it interesting. We just finished our unit on graphing Trig Functions, and now we're doing Trigonometry and solving non-right angle triangles using law of cosine, law of sine and we just learned about the Ambiguous case. Truly epic stuff. Conics was a good unit too. I told my teacher I found the max of tanx using a formula, then using that formula I gave him numbers to get the answer 1337. I got a couple laughs out if it. From the internet savvy people mainly :P. I've got a dry sense of humour.

[QUOTE="Bluestorm-Kalas"][QUOTE="I_pWnzz_YoU"][QUOTE="GabuEx"]

[QUOTE="DigitalExile"]This is like 9th grade math all over again. Damn teacher pulling brackets and letters from nowhere! I thought this was math! When did the alphabnet come into play? *Runs off crying*I_pWnzz_YoU

2 + 2 = 4

All better?

I thought it was 22 :?

No, 6+9=69

And here I was expecting to see a proof for 1 = 0, not 1 = 0!. :P

I like the whole 0.999... = 1 mind****, too.

GabuEx

Let x = 0.999...

10x = 9.999...

10x - x = 9.999... - 0.999...

9x = 9

Therefore x = 1

[QUOTE="GabuEx"]

And here I was expecting to see a proof for 1 = 0, not 1 = 0!. :P

I like the whole 0.999... = 1 mind****, too.

Red-XIII

Let x = 0.999...

10x = 9.999...

10x - x = 9.999... - 0.999...

9x = 9

Therefore x = 1

Yup, that's one of the proofs for it.

no... that is dumb.

there is a much better one.

a = b

a^2 = a*b

a^2-b^2 = a*b-b^2

(a+b)(a-b) = b(a-b)

(a+b) = b

a+a = a

2a = a

2 = 1

PROOF 2=1

of course, not really. cookie to the first guy who spots the error.

ah, using humaning thinking to define reality once again. Great idea, but not entirely true.EMOEVOLUTION

Lolz, I love it how some posters, after Shadow-syn's epic thread, pretends to have a superior way of thinking, and are able to understand the great cosmos. Some even claim to be aliens.

I have an open mind, so I don't rule out the possibility that some know the "real truth", but I have yet to see emoevolution back up any of his claims.

1=0 because Big Brother told me so.

Actually..i have seen these kinds of things before. There are many things in math that i don't understand..this being one of them.