Suppose that [math] \frac{1}{0} [/math] is a number. Now, look at the functional equation for [math] n! [/math] which is [math] (n+1)! = (n+1)n! [/math]. If we plug in [math] n=-1 [/math] we get [math] 0! = 0(-1)! [/math] and as [math] 0! = 1 [/math] this means [math] (-1)! = \frac{1}{0} [/math].
Of course, this entire argument follows from the incorrect assumption that division by 0 is valid. But remember we can only prove all polynomials have roots from the assumption that taking the square root of negative numbers is valid. So what does this mean It means there is a number system out there more powerful than the complex numbers. One of the great advantages of complex numbers is that we can take restricted functions (like the factorial, or the Riemann Zeta function) and then extend them to regions of the complex plane, where we can find beautiful identities that then translate in meaningful ways to identities about the original restricted functions. See where I am going at?
We could extend, in this case, the factorial function for negative integers (something not even the complex numbers can achieve) and then who knows what beautiful theorems will be found. This is why I suggest that complex analysis must stop being done, it is an incomplete theory. All the efforts of mathematics should be diverted to finding and constructing this missing piece of our number system.
>inb4 wheel theory Shut the fuck up fucking retard, wheel theory is useless for what I am talking about here. THERE IS A MISSING PIECE IN MATHEMATICS.
Carson Parker
So what are some nice properties of this 1/0?
Noah Long
Well, as I just showed you it would help us evaluate negative integer factorials. I am sure it will have many other properties, but it is hard to tell given that we don't have the right theory yet.
John Cruz
I thought you were building the theory
Sebastian Gomez
We have irrational numbers. We also have imaginary numbers.
And now is the time to introduce an entire new class: bizarre numbers. You saw it first here.
Dylan Mitchell
You didn't really evaluate anything though. It's well known that the gamma function has simple poles at the negative integers. You just wrote that as 1/0, which doesn't add anything new to the discussion.
Carson Butler
I am but this is bigger than me. It will take more than just one guy to do this. We need everyone constantly thinking about this.
Leo Murphy
There are hundreds of missing pieces in math. The world isn't a closed set
John Long
/thread
Jeremiah Rodriguez
Right so, fortunately, I am not talking about Complex Analysis.
Noah Brown
Okay, I don't know much of abstract algebra beyond the basics but this might be relevant to your post:
Yes, indeed. This is very similar but different. Just like a field with one element can't exist, a field with division by 0 can't exist either. So the goal is similar, looking beyond.
However, that goes more in the direction of algebra and geometry. I am talking about a new and bigger theory of analysis. Like Complex Analysis BTFO Real Analysis by being able to prove real results more beautifully, something very similar will happen with whatever is going on with 1/0.
Nicholas Rivera
I already thought about this 3 years ago. I discovered myself the equation for the newton bynomial with n exponents. Now I'm trying to find a function that includes the sucesions of the tartaglia pyramid.
Pathetic "whites".
Parker Ramirez
I look forward to reading about it
Anthony Walker
Link the paper if you're so hot
Gabriel Long
I discovered the newton bynomial formula in HS you colossal brainlet. What paper?
Jeremiah Lewis
>Suppose that 1/0 is a number. Which wheel are you working in?
Angel Reyes
The reason we accepted the imaginaries and the irrationals was because they weren't inherently contradictory. Division by zero can be shown to not be consistent, unless our previous assumptions don't work. For example, assuming that we can add 1 to [math]\frac{1}{0}[/math] we get [math]\frac{1}{0}+1=\frac{1}{0}+\frac{0}{0}=\frac{1+0}{0}=\frac{1}{0}[/math], [math]\frac{1}{0}+2=\frac{1}{0}+2*\frac{0}{0}[/math] but 2*0 is 0 so [math]=\frac{1}{0}+\frac{0}{0}=\frac{1+0}{0}=\frac{1}{0}[/math] and so it seems that every number equals zero.
Ryan Cox
Dividing by one is the same as dividing by zero: in either case, no work occurs. 36/1 = 36, we didn't divide 36 into any smaller parts. 36/0 = 36. We didn't divide 36 into any smaller parts.
Connor Cook
Are you retarded? Irrationals are contradictory in the set of rationals. (No irrational can be rational). The square root of -1 is contradictory in the real numbers (no real number exists such that its square is -1). That is why the arithmetic was EXTENDED to the irrationals, and then to the complex numbers. So just like you can extend numbers to include the square root of -1, there are ways to extend the arithmetic to include 1/0. You clearly don't know shit about math so please get out of my thread.
Joshua Myers
Please show some respect or I'm going to have to report your thread,
Oliver Sanders
Irrationals are not contradictory in a model of rational arithmetic, just nonexistent. That the model is incomplete does not mean it cannot be extended consistently. Division by zero leads to internal inconsistencies within the model.
Wyatt Bailey
the irrationals did not contradict the rationals in the exact same way the rationals did not contradict the integers. not being a part of a set doesnt mean that it contradicts the set. 1 equaling 0 is however, a blatant contradiction
Angel Garcia
The problem is that you still lose reflexive property of numbers.
1/0 = 0(-1)! Implies 1 = 0*(0*(-1)! = 0.
So defining it with some obtuse expression doesn't diminish that every number is the same in this scheme.
Ian Campbell
>THERE IS A MISSING PIECE IN MATHEMATICS. It's a feature, not a bug you brainlet. Not every number has a multiplicative inverse in every context. If you were working with mod 12 arithmetic you'd only have a quarter of your numbers where 1/x is possible for example (1, 5, 7, and 11). Just try seeing how many times you can add 2 to itself in mod 12 to get to 1, the answer is no amount of times will ever return that result. That's not a problem, you're just a retarded brainlet who had the same shit idea about treating 1/0 like the square root of -1 that every retarded brainlet has when he takes a high school math course.
James Green
Division by zero is inconsistent with the funamental properties of a ring you mong, you can't just make an extension of the integers like you can for other things. It's wheels or nothing.
Camden Mitchell
>when reddit comes to sci
Gavin Evans
Why do brainlets argue so hard over that word 'zero' when 0 is just a numerical glyph that every mathematician can agree on?
It's like you guys can't understand the difference between a fixed-width glyph and a 'concept that your parents had to tell you otherwise how else would you guys be posting on a Quantum-Field-Operational-Server'
Oliver Hill
division by zero is perfectly ordinary so long as you're willing to sacrifice field properties
e.g. real projective line
Dominic Hall
lol I have better things to do.
Gavin Garcia
eat shit newfag
Brody Brooks
Which you SHOULD be willing to do if you want anyone to exchange field properties.
被零除是非常普通的,只要你願意犧牲字段屬性
例如 真正的投影線
Luke Peterson
90^-9 = 1/90^9
Nathan Carter
Please stop existing.
Bentley Murphy
'Please' is not recognized as an internal or external command, operable program or batch file. // '請'不被識別為一個內部或外部的命令,可操作的程序或批處理文件。
>Implying non-existent = inconsistent You really are the lowest type of dense retarded brainlets. Kys.
Anthony Rodriguez
>言下之意不存在不一致= 你真的是最低屬於密集智障brainlets的。的KYS。
Isaiah Scott
醉箱
Juan Long
Stop talking in chinese, most people on this board won't understand you, which ruins the discussion.
____
Sale enculé nique ta race tu dis un autre mot de chinois et je t'encule fils de pute.
Landon Wood
Kek, I think he was banned. All his posts were deleted and also his thread.
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*risos* Eu acho que ele foi banido. Todos seus posts foram deletados, tal como seu thread.
Austin Harris
>fils de pute. I just realised you were actually were cursing at him. In this case, he is a big filho de uma puta do caralho que tem a buceta parecida com um elástico frouxo.
Luis Gray
PORCO DIO E LA MADDONA TROIA FARCITA DI SBORRA CУКA БЛЯT EБAT EГO HA ХУЙ
Jordan Hughes
We already allow division by zero in the form of complex infinity.