Tell me why this meme is still perpetuated in mathematics. inb4

take the limits fag
dividing by a number less than 1 is the same as multiplying
answer to a is infinite cakes
answer to b is 0x infinichan =1

More like trying to divide a cake equally by cutting it into slices with a width of 0

>>7693878
only fair...

>>7693871
>dividing by zero is the same as dividing by one
This might surpass Terryology in terms of retardation

>>7693871
You cannot divide by "zero" in the field of real numbers equipped with addition and multiplication because zero has no multiplicative inverse.
i.e. there does not exist a unique element x in the set of real numbers such that x(0^-1) = 1, where 1 is the multiplicative identity.
It is true that 0(0^-1) = 1, but it is also true that 0(0^-1) = y, for all y in the set of real numbers.

It is however completely possible to create a field where we can "divide" by "zero".

>>7693881
Make two cuts in the exact same spot. There, you cut a slice with width 0 i.e. nothing. You have the whole cake left over, so your result is the whole cake.

Trying to create a bijection between the division of numbers and "real life objects" is definitely NOT a good idea since this fails to explain more abstract concepts such as the division of negative numbers.
For example, why is the division of two negative numbers a positive number (using "real life objects")?

>>7693871
>cut a cake into 0 parts
>you get 1 cake

>>7693915
No, if there are zero parts afterward, that would mean you destroyed the cake, because you originally started out with one part.

>>7693871

You can't cut a cake into zero parts, there would be no cake it would not exist. To cut into 3 pieces, make 2 cuts, to cut into 2 pieces, make 1 cut, to cut into 1 piece, make 0 cuts leaving the cake intact in one piece, to cut into 0 pieces the cake dissapears and you don't know how many times you could have possibly cut into it since poof gone

If you don't understand this maybe you should go collaborate with terrance howard on a theory or something

Funny how you accuse me of regurgitating elementary shit when your whole concept of division is based on elementary-level analogies.

>>7693871
You have to think that, the smaller the number that you use as the denominator, the bigger the result will be (i.e., divide any number by 1, and you get the same number, divide it by 0.5, and you get the double, divide it by 0.25, and you get the quadruple and so on). Thus, when the denominator gets to 0, you get an unmmesurably big number, which is infinite.

Here:

>https://en.wikipedia.org/wiki/Wheel_theory

Read it. If you don't understand it, you are not allowed to discuss why we can't divide by zero.

>this many responses to bait
Never change, /sci/.

>>7693913
Do negative numbers even exist in purely physical terms?

>>7693900
aggressively ignorant tbhfam

Reminds me of this sjw crusader in my proofs class who said she didn't believe in the concept of 0. FOH with that bs.

>>7693871
If you allow people dividing by zero you literally break the mathematics system by proving that 1 = 2.

>>7694027
That is the point of the question.
I'm trying to get across the absurdity of this entire thread trying to make sense of division with this cake cutting nonsense.

>>7693878
ISLAM NINJA FORCE GO

>>7693871
>regurgitating shit their elementary teacher fed for them, and can't think for themselves.
>implying Opie isn't just the smartest person to come along in the last few thousand years, but he also expects *you* to be smarter than the aggregate of all mathematicians ever.

>>7693871
>cut a cake into 0 parts, you get the original cake because you didn't cut it into anything
>>7693900
>You have the whole cake left over, so your result is the whole cake.

if 1 cake divided by zero = 1 cake, then zero times one cake = one cake
I has zero, can I has free cake?

File: 1365905463019.jpg (449KB, 1024x630px) Image search: [Google]

449KB, 1024x630px

>>7693871
... except that zero is infinitely suspendable do to it being subject to the traditional location of everything

People really just don't think rationally when they consider nothing, to much fear of it, the thought of it being at all angers them not to mention the pain of loss that it also implies and the sadness of not having anything
When in reality the fabric of nothing bares the weight pain fear anger and sadness of something that does exists in its feeling of abandonment resentment and sadness of such not to mention the fear of translation which nothing as a thing that can simply be conceived of as simply 'idea' is that that proves that all of these things are moot by affiliation of discovery compared to subjection of which means that anyone who considers nothing not just an affiliation of sentience is a fucking idiot
Sorry to be so blunt/rude but our civilization is acting like a bunch of toddlers in the reaction to their parent at the moment and it's annoying af

>>7693871
Graph 1/x
If you go from the positive side you will conclude that 1/0 approaches infinity.
If you go from the negative side you will conclusde that 1/0 approaches negative infinity.

That is just the first problem.

Graph 2/x and you will see that 2/0 also approaches infinity and negative infinite

The same for any n/0

That is not well defined.

What can you do though?
Well, 0 factorial does not follow the usual pattern of factorials. We just agree that 0! = 1 because that is helpful in proving theorems about factorials without having to include exceptions.

Can you provide enough solid evidence that giving a "special" definition to n/0 would actually help us prove new important theorems and also reduce the need for special cases?

>>7694035
>Reminds me of this sjw crusader in my proofs class who said she didn't believe in the concept of 0
.........How does she reject the idea of zero in a way related to social justice?

>>7693900
>You have the whole cake left over, so your result is the whole cake.
Are you seriously confusing a quotient with a remainder?

>>7694018
That's a cheap way to go about it. If you dint care about associativity you can have a multiplicative inverse for 0 without resorting to this "well it's not actually the inverse operation of multiplication, just a one sided..."

>>7695761
1=penis
0=vagina

>>7695944
Is this a joke or actually what her reasoning is? I could honestly see it going either way.

>>7693896
This. But then we lose a lot of the nice properties of vector spaces.

>>7695405
1 * 0 = 0
subtract 1 from both sides
(1-1) * (0-1) = -1

0 * (0 - 1) = -1
0 * (-1) = -1
0 = -1

solved. 0 has actually been -1 all along.

>>7693896
Shouldn't the inverse be infinity? In keeping with their cake metaphor, it'd be like slicing in the same spot over and over forever. Thus, shouldn't dividing by 0 equal infinity?

>>7697509
>(1-1)*(0-1) = -1
should be
(1*0) - 1= -1

>>7697518
DO NOT use the cake metaphor, it really is useless. Can it explain negatives? Can it explain other fields? Does slicing a negative cake a negative amount give a positive cake?
A lot of non-concrete/non rigorous discussion can be had about cake and slicing, but if it's wrong in one place, what's to say it's correct anywhere?
Anyway, digression aside, if ∞ is the inverse of 0, then we can write:
0(∞^-1)=1
0 = 1(∞)
0 = ∞
In which case, this "∞" thing is actually 0.
And again we come back to 0 being the inverse of 0, blah blah (see the end of the post you quoted).
Did you perhaps confuse this with the limit of 1/x as x tends to infinity being 0?

>>7697518
If only Real Numbers were defined as easily as a cake.

>>7697547
This.

>>7693913
>Trying to create a bijection between the division of numbers and "real life objects" is definitely NOT a good idea since this fails to explain more abstract concepts such as the division of negative numbers.
>For example, why is the division of two negative numbers a positive number (using "real life objects")?
Sort of makes sense. If you have a negative stake in a negatively priced equity then you are entitled to a positive sum of money. That is to say if you've bet against something and its net change is down then you get cash.

>>7697590
You're implicitly using the fact that negative divided by a negative gives a positive there.

>>7697601
That's my point; that it makes sense in real life as well.

>>7697609
But that's not my point.
I'm asking for an analogy using real life objects, such as this cake nonsense.
Of course it makes sense when you use actual numbers.

>>7697624
Perhaps cakes are a scalar quantity and thus to speak of negative cake, or portions thereof, makes no sense?

>>7697636
Indeed!

>>7693871
>"HURR DURR U CANT DO IT CUZ U CANT!"
But it's defined that way on the reals.

Though I do agree that this suggests a natural & necessary extension to the reals.

>>7693871
You can't divide something by nothing

>>7697791
>You can't divide something by nothing

>You can't take the square root of 2, there is no quotient of integers which corresponds to this quantity

>>7697841
But you can get infinitely close to the solution for a square root of 2

>>7697846
Can you fill in the blanks?

>As you divide something by a l_ _ _er number, the result gets s_ _ _ _er
>Thus, when dividing by the l_ _ _est quantity, the result is the s_ _ _ _est quantity

Division by zero is impossible and we can prove this using contradiction. Presume that [math]z = \frac{1}{0}[/math], so that [math]0z = \frac{0}{0} = 1[/math]

[eqn]0z = 1[/eqn]
We multiply 2 by both sides; simple algebra.
[eqn]2(0z) = 2 \times 1[/eqn]
Multiplication is associative, so we rearrange the order.
[eqn](2 \times 0)z = 2 \times 1[/eqn]
Multiplying two by zero produces zero.
[eqn]0z = 2[/eqn]
A contradiction is reached.
[eqn]1 = 2[/eqn]

>>7697883
Except that 0/nothing still applies nothing in division

.000∞1 is still something

>>7697893
Note that the contradiction reached in this proof is NOT unique.
Indeed, 0/0 can be any number you want.

>>7697925
Yes. Allowing division by zero lets you make any number equal to any other number. A high school math teacher told me that a long time ago, but I never understood why until I learned what proofs were in college.

>>7697930
>Allowing division by zero lets you make any number equal to any other number

Rather, 0/0 is an indeterminate form (as is infinity/infinity, -infinity/infinity). This means that 0/0 can be equal to any number (hence the name).
Observe:
Let x = 0/0
Then 0x = 0
So any number x satisfies this.
Indeterminate forms are NOT to be confused with undefined forms such as 1/0.

>>7693871
So following your cake analogy, how do you explain in simple words dividing the whole cake by 1/2,1/3,1/4.... instead of dividing it by 1,2,3,...? Cuz if you start doing that, youre gonna approach to the infinity that some of us think you should get close to, unless it's a cake from neverland or some shit like that.

>>7697942
>indeterminate form
no one mentioned calculus or limits, stop.

Dividing by zero makes math a lot cooler. To be consistent, 0*1 would have to be different from 0*5. It's about time we give it the complex number treatment, tbqh.

>>7698232
We're considering analysis here, having calculus or limits mentioned is inevitable.
It doesn't make the explanation any less valid.

>>7698262
it's not an explanation. 0/0, as in dividing number 0 by 0, has nothing to do with a junk, meaningless result you get when you attempt to evaluate a limit in calculus which looks like 0/0 but means "you fucked up".

>>7698279
>number

File: 1448782003134.jpg (48KB, 469x505px) Image search: [Google]

48KB, 469x505px

What the fuck is up with this shitty /b/ tier analysis of division by zero these days

wutf get drugs n get it noob

>>7693871
HURR DURR U CANT DO IT CUZ U CANT!

>>7693871
>cut a cake into 0 parts, you get the original cake because you didn't cut it into anything
>cut nothing into 0 parts, get nothing because you did nothing to nothing

You mean 1 parts.

you cant cut a cake into 0 parts faggot

>cut cake into 3 parts requires 2 cuts
>cut cake into 2 parts requires 1 cut
>cut cake into 1 part requires 0 cut
>cut cake into 0 parts requires -1 cut

you have to let the cake cut you in other words