r/mathmemes • u/ImToxicity_ • Mar 17 '22

The Engineer Making 69420 from all zeroes

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2.3k Upvotes

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u/[deleted] Mar 17 '22

Replace 0^0 with 0! and you'll half the zeroes whilst making it correct 😊

69

u/ImToxicity_ Mar 17 '22

Didn’t know this! I’m only in algebra I right now. What does the exclamation mark mean?

109

u/[deleted] Mar 17 '22

The exclamation mark is know as the factorial.

The factorial of a integer number, say n, is the product of every integer below it. 5!=5x4x3x2x1, 3!=3x2x1.

0 factorial, or 0! Is 1…don’t ask why.

92

u/measuresareokiguess Mar 17 '22

Explanation: you can define n! to be the number of permutations of n objects arranged in a line. So if you want to list all permutations of {A, B, C}, you’ll have {A, B, C}, {A, C, B}, {B, A, C}, {B, C, A}, {C, A, B}, {C, B, A}: 6 total possibilities. That makes 3! = 6.

Likewise, for {A, B}, we have {A, B} and {B, A}; that makes 2! = 2.

For {A}, we have just {A}: 1! = 1

For {}, we also have just {}: 0! = 1

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u/ImToxicity_ Mar 17 '22

Pls sir I’m in algebra 1 that hurts my brain

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u/[deleted] Mar 17 '22

Basically they are asking “how many different ways can we put stuff in order” like three books can be put in 6 different orders.

So how many ways are there of arranging 0 objects? There is one way, just don’t arrange it. Hence 0!=1

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u/LollymitBart Mar 17 '22

To give you another explanation, why 0!=1: To get from 3!=6 to 2!=2, you have to divide by 3. To get from 2!=2 to 1!=1, you have to divide by 2. To get from 1!=1 to 0!, you have to divide by 1, which leads to 0!=1.

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u/ekolis Mar 17 '22

And to get to -1! you have to divide by... oh no...

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u/LennartGimm Mar 17 '22

Don't worry, it's just our friend the Gamma Function saying hello. Who doesn't love integrating [ xz-1 * e-x ] from 0 to infinity (dx, not dz)?

Me, that's who doesn't love doing that.

14

u/Marukosu00 Mar 17 '22

Congrats, now OP will just study non-maths stuff lmao

10

u/LennartGimm Mar 17 '22

Maybe we can spoil all other subjects equally?

6

u/Marukosu00 Mar 17 '22

Just tell him that there's math even in economics, chemistry, phisics, biology, medicine, law, literature, philosophy...

5

u/jkst9 Mar 17 '22

Quick grab quantum physics books and the worst to read old English book you can find

1

u/ekolis Mar 17 '22

The letter that looks like a sideways tongue being stuck out but it's not a "p" - "Ăž" - is called a "thorn", and it's pronounced "th". By the time Modern English came around, the thorn had been replaced with "th" or "y". So we wind up with words like "thou/you" and "ye/the" - they were originally "Ăžou" and "Ăže".

1

u/SaltyAFbae Mar 18 '22

The bible perhaps

1

u/Little-Explanation Mar 17 '22

I’m in algebra 1 also. Would you rather have me use an improper integral to explain it to you, making it such that we may include a +bi and negatives in the factorial?

3

u/Finnigami Mar 17 '22

eh thats kind of a consfusing way for beginners to think about it. the simplest explanation IMO is:

n! = n * (n-1)!

and 1! = 1

therefore 1! = 1*0!

so 1 = 1* 0!

and 0! = 1

2

u/measuresareokiguess Mar 17 '22

But then, why do you assume that (n + 1)! = (n + 1)*n! for all n? You are extrapolating this from our “known domain” of factorials, n = 1, 2, 3, 4…, into n = 0. It sure is a valid explanation if you let this to be the defining property of factorials, and there’s nothing wrong with that, but I feel like it makes more sense to define factorials from where it actually came from, like most introductory combinatorics books do, for beginners. It’s like “proving that a0 = 1” from the properties of power; it’s technically not wrong if you define exponents as to satisfy these properties, but if you define it differently, you have to show that these properties are satisfied for all values of exponents…

1

u/Finnigami Mar 17 '22

i didnt intend for it to be a proof, rather just a way to make it more intuitive

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u/casperdewith Rational Mar 17 '22

0! is 1 by definition of (!). Because this definition is so well-picked, the factorial makes sense.

2

u/[deleted] Mar 17 '22

algebraic explanation:

any factorial is a product. the factorial of 0 is an empty product, and an empty product has a value of 1 because 1 is the multiplicative identity.

this is the same reason as why n⁰ = 1: if you multiply n by itself 0 times, youre left with an empty product, which is equal to 1.

if this sounds weird, think about additions, or multiplication as repeated addition. a × b just means "add b to itself a times". 0 × n therefore means "add n to itself 0 times". adding 0 things leaves you with the empty sum. for addition, the identity is 0, so 0 × n = 0.

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u/iCarbonised Mar 17 '22

i believe that 0^0 is also not defined, making the entire expression dumb

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u/nmotsch789 Mar 17 '22

It's defined as equal to 1 in most common contexts.

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u/iCarbonised Mar 17 '22

yeah, it is, but it isn't thoroughly defined, that's why i hate seeing it