/sci/ - Science & Math

Think about it like this:
2/y=x so 2=x*y
let y=0
2=x*0
2=0 which is a contradiction.

or just look at the graph of f(x)=1/x, vertical asymptote at x=0

>>2178853
That means that numbers are not consistent with each other. They must satisfy the required properties like zero being a point that much be reached if a line is constantly moving towards it without any condition to slow it down. You can't even slow down a function. That's just silly.

I hate this definition of math. I wish I could just go to the future where this isn't an issue. Calling it undefined is just cheap.

>>2178876
Why is calling it undefined cheap? Is 1/0 going to be defined in the future? Also, a function does not need to be defined at all points.

>>2178904
How would you know if a function doesn't need to be definable on all points? Have you seen all forms of application for functions?

multiplying is way different from dividing

>>2178912

Suppose all functions can be defined at all points.
f(x)=1/x is not defined at x=0
Contradiction
Thus, all functions are not defined at all points.

Didn't Newton figure out how to divide by zero?

>>2178786
>If you can only divide by a non-zero number, why can you multiply by a zero number?

look at how division is defined and it is self evident.

>>2178786

>why can you multiply by a zero number?
You can't.
You cannot add, subtract, multiply or divide by zero. Zero isn't a number, it's a concept. It's like infinity. Anything plus infinity is infinity. Infinity minus anything is infinity. Anything time infinity is infinity, and infinity divided by anything is infinity. In the same way, 0 does nothing, or creates nothing.

all op says is infinity=infinity, which is true

>>2178960

you can add, subtract, and multiply by zero, just not divide by 0.

>>2178975

1/0 =/= infinity

OP division by zero is defined in many number systems

see projective line, and see riemann sphere.

http://en.wikipedia.org/wiki/Real_projective_line

http://en.wikipedia.org/wiki/Riemann_sphere

so calm the fuck down

>>2178960

zero is a number. one of the axioms of real numbers is that there is a unique element 0 belonging to R such that 0+x=x for all x belonging to R.

One divided zero times is one. What do I win?

>>2178978
But if it does absolutely fuck all, can anything really have been done?

When you divide, you take something and separate it into "groups" 10/2 = 5, separating 10 into two groups of 5
Multiplying is reverse, putting two groups together, 2 x 5 = 10, which is putting two groups of 5 together to make 10
You can multiply by 0 because you are taking a group of n and having 0 groups of n, thus 0

But how the fuck do you divide something into 0 groups. makes no fucking sense

>>2178999
TRIPS, it must be true!

>>2179000
>>2179018

>>2179000
multiplying by zero doesn't do fuck all, it kills things dead

it's also useful for counting from negatives to positives. everything would be fucked up if the difference between 3 and - 3 was 5

seeing as zero sums are everywhere in maths and in life, it is profoundly useful for problem solving.

7/10 by the way

>>2178986
http://en.wikipedia.org/wiki/Real_projective_line
>This structure, however, is not a field, and division does not retain its original algebraic meaning in it.

As for Riemann Sphere, this is an extension of the field of complex numbers where infinity has been added and 1/0 has been defined as infinity. however 0/0 and 0*infinity are undefined.

>>2179048
>states the fucking obvious

OP asked for div by zero

i give it

>>2179063
>states the fucking obvious
That was obvious? I didn't realize that The Real Projective Line and Riemann Spheres are common knowledge....

>>2179107
obvious to anyone who brings them up in a discussion about division by zero retard

>>2179154
>obvious to anyone who brings them up
You brought them up so I would hope it would be obvious to you. I gave a quick explanation for others. U mad?

>>2179194
then don't quote me and link my post if it's for others/general discussion

lrn2 4chan

>>2179245
I quoted the wikipedia article you posted, not what you said. Also, I linked your post because I was commenting on it.

We all know that 2*0=0 , 2342*0=0.
Anything that is multiplied by zero is zero.
But exponents work like this, and is WRONG.

3^3=3*3*3=27
3^2=3*3=9
3^1=3*1=3
3^0=3*0=1

problem Newton?

>>2179306
are you still discussing this shit?

>>2179330
you mean they work like this
3^3=3*3*3*1=27
3^2=3*3*1=9
3^1=3*1=3
3^0=1=1

yours had a combo breaker on the last line

see also 0!

>>2179333
Yes.

6/3=2
6 is torn in 3 pieces = 2

6/2=3
6 is torn in 2 pieces = 3

6/1=6
6 is torn in 1 piece= 6

6/0=0
6 is torn in 0 pieces=0

Its the same logic with multiplication, why it isn't applied in division?
Why not?

>>2179346
You only prove that you dont know shit about math, and you dont have critical thinking, you accept anything your teachers tell you.

Am not him, and i agree with 3^0=1

Am saying you dont KNOW why its 1.

>>2179368
psycho detected

see empty product

>>2179354
Well, i dont know.

if i have a pie and divide it into zero (portions) i end up with zero pie?

i don't understand.

inb4:

5/0=?
?x0=5

Algebraic interpretation

It is generally regarded among mathematicians that a natural way to interpret division by zero is to first define division in terms of other arithmetic operations. Under the standard rules for arithmetic on integers, rational numbers, real numbers and complex numbers, division by zero is undefined.
Division by zero must be left undefined in any mathematical system that obeys the axioms of a field.
The reason is that division is defined to be the inverse operation of multiplication. This means that the value of frac{a}{b} is the solution x of the equation bx = a whenever such a value exists and is unique. Otherwise the value is left undefined.

For b = 0, the equation bx = a can be rewritten as 0x = a or simply 0 = a. Thus, in this case, the equation bx = a has no solution if a is not equal to 0, and has any x as a solution if a equals 0. In either case, there is no unique value, so frac{a}{b} is undefined. Conversely, in a field, the expression frac{a}{b} is always defined if b is not equal to zero.

now don't let them totally fool you....
It is possible to disguise a special case of division by zero in an algebraic argument, leading to spurious proofs that 2 = 1 such as the following:

With the following assumptions:

0\times 1 = 0
0\times 2 = 0

The following must be true:

0\times 1 = 0\times 2

Dividing by zero gives:

frac{0}{0}\times 1 = frac{0}{0}\times 2

Simplified, yields:

1 = 2\,

The fallacy is the implicit assumption that dividing by 0 is a legitimate operation with 0 / 0 = 1.

Although most people would probably recognize the above "proof" as fallacious, the same argument can be presented in a way that makes it harder to spot the error.
For example:
if 1 is denoted by x, 0 can be hidden behind x − x and 2 behind x + x. The above mentioned proof can then be displayed as follows:

(x-x)x = x^2-x^2 = 0\,
(x-x)(x+x) = x^2-x^2 = 0\,

hence:

(x-x)x = (x-x)(x+x)\,

Dividing by x-x\, gives:

x = x+x\,

and dividing by x\, gives:

1 = 2\,

The "proof" above requires the use of the distributive law. However, this requirement introduces an asymmetry between the two operations in that multiplication distributes over addition, but not the other way around. Thus, the multiplicative identity element, 1, has an additive inverse, -1, but the additive identity element, 0, does not have a multiplicative inverse.

>>2179346
>see also 0!

wasn't 0! defined to be 1 more because shit doesn't work if it isn't than because it makes logical sense?

>>2179354
Splitting a number into n equal parts is not division. It is a lie they tell dumb children to help them understand division.

division is the inverse of multiplication, where it exists.. you can multiply by zero, because multiplication came first... you cant divide by zero, because there are infinite solutions, hence the inverse doesn't exist

>>2179354
if I see you tear something into zero pieces, I'll believe you

>>2179414
Truth. Most math classes are full of small lies so people can wrap their heads around things. For instance, they teach that sqrt(-1) does not exist; then later they teach about complex numbers.

>>2179412
it's the empty product

which makes perfect sense to me

>>2179412
0! naturally equals 1, if you don't include 0, factorials are only defined on positive integers (n! = PI(i = 1 to n)n)
>yeah, I don't know how to fancy text capital pi and shit...

>>2179430
There are not infinite solutions. There is no solution.

I believe in elementary mathematics, functions are not, in theory, bijective.
As such, 0 can be the result of a multiplicative case but not a divisive one (and is thus undefined), and as such it can not be divided by (undefined).

>>2179442
>taught that sqrt(-1) does not exist
Up until grade 4 or 5 I believe. The bare concept of complex numbers (specifically imaginary numbers therein) isn't very complicated and I don't think I had many classmates struggling with it. The 'equal parts' split is usually abandoned the following year after even learning division, if not later in the same year.

"i can't tear a cake into 0 pieces lol that doesnt make sense" sames GOES FOR 0*n YOU STUPID CUNT.
I could easily say "0*5? whoa how can i multiply my apples with nothing? that doesnt make sense "

As with 0+1 you can't practically add something to zero or multiply something with zero or divide something with zero.
But at you CAN mathematically add, subtract, multiply by zero but you can't divide with zero because our math system is flawed and because it doesnt make sense logically with stupidly people think its the reason.

Also someone said that n^0=1 cause it doesnt work otherwise.
That means one thing: That it is FLAWED and AM RIGHT.

You are prententious fucks with 0 thinking just reading like sheeps.

trololololol

>>2179491
>But at you CAN mathematically add, subtract, multiply by zero but you can't divide with zero because our math system is flawed and **NOT** because it doesnt make sense logically with stupidly people think its the reason.

fixed

>>2179438
>if I see you tear something into zero pieces, I'll believe you

you aren't the brightest are you.
ohyou.jpg

>>2179491
I don't see any problem with taking 5 apples zero times or taking zero apples 5 times... I can take nothing all I want and still have nothing... same concept for adding/subtracting zero... I can give you nothing, and you'll have the same shit you had before..

>>2179500
thats my point..

>>2179491
also, n^0 is 1, because it is something multiplied by itself 0 times... hence it is just the multiplicative identity 1

>>2179503
??

>>2179513
>multiplicative identity 1
>mfw
How does it feel to understand math like a woman?

The _definition_ of division is that it's by a non-zero number, and it has to be in a ring where every element has a multiplicative inverse, so that a * a^-1 = 1. There is no ring in which 0 has a multiplicative inverse, so division is always defined for all elements but 0.

>>2179516
Nah, you wont get it anyways.

>>2179412
N! is the number of ways to stack a deck of N unique cards.

There is only one way to stack a deck of zero cards. You just don't stack it.

things like 0^0 and 0! aren't really provable, it's just useful to have them defined as 1. stuff like the binomial expansion only works when 0!=1

>>2179538
Same applies to multiplication, you are too blind to see it cause it fits with the current maths we all know.

Hey guys
STOP FEEDING THE FUCKING TROLLS
You cannot divide by 0, this is fact
you guys are buttshit retarded, all y'alls

Alright, this question isn't really answerable unless you bust out the Field Axioms.

Specifically, the additive identity 'zero', multiplicative inverse, and distribution over addition. Suppose the multiplicative inverse axiom did not exclude zero from having a multiplicative inverse. Then, the following statements would be true:

a + 0 = a = 0 + a
(a+b)c = ac + bc
0 * 0^-1 = 1

For brevity, let Z be the multiplicative inverse of zero.

Now, let us consider a + 0 = a. Multiply both sides by Z. We get aZ + 0Z = aZ. But, 0Z = 1, due to the "we can divide by zero" version of the multiplicative inverse axiom. So we replace, and get

aZ + 1 = aZ

Add in the additive inverse of aZ, and we wind up with 0 = 1. This is obviously not true for the real numbers, or for any other non-trivial field (there are trivial examples you can use, but that gives algebraists a bunch of headaches when generalizing over all fields, so the field axioms generally also include 0 != 1)

tl;dr version - with numbers and algebra that works like you'd expect it to, if zero multiplied by any number is equal to one, then you can prove that 0 = 1.

>>2179607
So you are saying they broken a rule cause another part of the 'book' was already broken.
In the end its more convinient that way.

Not at all. In a mathematical sense, dividing by zero is the same as multiplying by 0^(-1). Multiplying by zero is just multiplying by 0^(1). 0^(-1) is undefined. 0^(1) is just 0.

>>2179548
0^0 is easily provable.
Just consider f(x) = x^0. Calculate the limit g(x) as x approaches 0. g(0) = 1.

for everyone wondering why n^0 = 1 (for all n of the R):

n^-1 * n^1 = n^0 (addition of exponents when multiplying same base)
n^-1 = 1/n
n^1 = n/1
therefore, our original equation is transformed:
n^-1 * n^1 = 1/n * n/1 = n/n
n/n IS EQUAL TO ONE
therefore, n^0 is always equal to 1.

just in case anyone wanted to know.
as for division by zero, it's obvious it's impossible for many reasons, all of which have been stated already.

>>2179607
>Now let us consider

lol... next