division by zero should technically give infinity, but that makes it posibble to make any 2 arbitrary numbers equal so it is defined as "undefined" instead.
what part of "in the zero ring" do you not understand. gb2/algebra/ lol
Name:
Anonymous2006-01-10 4:33
oh anonymous, come back when you know galois theory.
Name:
Anonymous2006-01-10 13:31
1/0=infinity
Name:
Anonymous2006-01-10 14:17
a/0 is undefined, for a<=R
not the same as infinity...srsly guys.
Name:
Anonymous2006-01-10 14:58
infinity isn't a member of the reals
Name:
Anonymous2006-01-10 16:21
>>6
actually a < £$^WRY$£&W%YQ£YA$%&Q%UW$W%&OS*$U+-=-=-=w46q"$^
Also, if you can't understand the above equation you are an idiot.
Besides your argument is completely irrelevant. A simpler counter-argument would have been that no number of 0s added together will make anything other than 0, therefore when you divide by 0 it doesn't make infinity.
Name:
Anonymous2006-01-10 16:25
In fact a better argument would be that 0 isn't a real number.
Name:
Anonymous2006-01-10 17:10
wow, you guys are nerds... actually, not even. just a bunch of loser virgins.
What has Galois Theory to do with anything? In the zero ring, there is only one element 0, which is the multiplcative and additive identity. We have 0/0 = 0 in the ring. This is consistent with multiplication and addition in the 0 ring.
Name:
Anonymous2006-01-11 2:32
division isn't defined in rings... only fields. fail.
>>13
well i just defined it bitch. what you going to do about it.
Name:
Anonymous2006-01-11 3:03
you can't define division by the additive identity. ever. even if it makes sense.
Name:
Anonymous2006-01-11 3:47
>>16
these people are noobs. zero ring is just some faggot idea made up to explain that OMG a/0 IS POSSIBLE RLY! They keep going off using the wrong math and trying to use that to explain something WAAY over their heads.
>>6 is correct, it's just that idiot >>8 read it wrong. it's not a "less than/equal to" sign. It should read as set notation like that small looking e. LOL moron.
>>9 0 belongs to the reals and nobody except failed nerds will argue that.
Also if 0 is a real number you should be able to divide other numbers by it.
Divide something by 0 to prove you are not a fucking idiot and probably gay. Failure to do so will be seen as an admittance of this. You have 24 hours.
Seeing as you are sure you are right this shouldn't be hard. If you fail it probably means you are gay.
Oh wait, just because it's a ring it can't be a field? GTFO >>17
Read more, division by 0 is possible in the 0 ring because 0 is the only element in the ring and 0 is it's own multiplicative as well as additive identity.
so we have 0 + 0 = 0
0 x 0 = 0
0/0 = 0
Anyway, right now it looks like the focus has been shifted to showing that 0 is in the real number system. But smart people already know this and DON'T require proof. *rolls eyes* We'll leave this snack to you noobs. :)
Name:
Anonymous2006-01-13 13:47
>>23
wait, but I just showed you 0 has an multiplicative inverse in the 0 ring. Prove me otherwise. Just because a ring isn't a field doesn't mean there doesn't exist elements in the ring which are invertible.
Name:
Anonymous2006-01-13 16:05 (sage)
>>25
ZOMG you useless cunt. Either shut up or stop breathing. The shit pouring out of your mouth has absolutely no point, even in the already abstract world of maths.
In fact I can say that I create an arbitrary system where division by 0 is a valid operation which results in infinity. Who gives a fuck? It's arbitrary you fucktard.
Name:
Anonymous2006-01-13 17:36
>>26
We're talking about a ring with only one element you retard. Who gives a shit about infinity.
Name:
Anonymous2006-01-14 8:15
>>27
Forget that idiot >>26 . He keeps posting wrong shit about infinity because he thinks he elarned math from the wiki.
Name:
Anonymous2006-01-14 8:17 (sage)
>>28
WRONG shitface, that was my first post in this thread.
Seriously guys, just stop pretending you can think and shut the fuck up already.
God, why do terrorists target businessmen who actually DO something with their lives, when they should be putting you dumbfucks out of your misery.
Name:
Anonymous2006-01-17 13:45
well it´s not really hard is it:
lim(1/x)for x->0 results as a positive or negative infinity.
on the other hand: lim(1/x²) for x->0 results only in a positive infinity.
you just have to look at the graph of it:
we all know x^0 is allways 1 and because of this you can say that
x^0=1 for x element of R without 0
and 0^0=1 for x=0
Name:
Anonymous2006-01-17 17:28
>>37
we're talking about the zero ring here. The 0 ring consists of only 0. if by 1 u mean the multiplicative identity then yes 0/0 = 1 = 0 because in the zero ring 0 is both the additive and multiplicative identity.
Name:
Anonymous2006-01-18 16:08
>>37 >>38 is a Fag. I have no idea where R came from and it suggested nothing to imply x^0 = 1 when x isn't 0. x^0=? is a mathematical model and ? means what do you have to multiply by itself infinite times in order to get x.
If you want to find what you have to multply by itself 3 time to get x you do x^(1/3), if you want to find what you have to multiply by itself 800 times you do x^(1/800). As you might guess anything divided by infinity is 0, therefore...
x^0=x^(1/infinity)
of course there are certain rules which determine what happens when you multply something by infinity and it revolves around -1, 0 and 1.
Seeing as 0 is not a real number, there can be no real answer to x^0, unless x is also not a real number. Yes, everyone in the entire world is wrong except me. However everyone in the world is right about 0^0 = 0
0^0 = 0 because you can multiply 0 infinite times and you still end up with 0
infinity^0 > 1
1 < (infinity and -infinity)^0 < -1
-1^0 doesn't exist like other rooted negative numbers (1/infinity, remember?)
1^0 = 1, 1^anything = 1 of course
Name:
Anonymous2006-01-18 16:33
what the fuck?
0^0=1 by definition
0 is a real number
i'm not even going to try to make sense of the rest. jesus fucking christ, you 12 year olds that think you have it all figured out.
I am not talking about reals you idiot. I am talking about a 0 ring. A ring with one element. Which is it's own multiplicative and additive identity. There is no point thinking about operations with other elements which are not members of that ring. Please learn some algebra and come back
>Seeing as 0 is not a real number
of course it is, and again I wasn't talking about reals.
The 0 ring is absolutely useless you cunt. I can't believe you've been hammering this on for so long. Just do us all a service and go fucking hang yourself.
i think he meant that all numbers^0=1 because we all know 2^0=1;
20^0=1 and so on; so if we take a look at the graph of the function f(x):x^0=? we see that it is a constant with y=1 and no other thing
oh wait, is that all you can say about the 0 ring? I am not saying just because it's possible to divide by 0 in the 0 ring, that you can divide in a bigger ring. K THANKISBYA
Name:
Anonymous2006-01-19 12:30 (sage)
>>47
Jesus H. Christ. We know what you're saying. The thing is, NOBODY CARES.
x/0=? is like saying, "how many nothings are there in something?" So really, the answer is none or, 0. To say that "zero isn't a real number" doesn't mean much because the purpose of a number is to explicitly describe some measurement of a quantity. For one to suggest that a number is anything more significant (as if 1 or 2/3 are anything by themselves) is to demonstrate that one has been indoctrinated with intuitism, and really never clearly understood or deduced anything in ones life. ok bitch on...
Name:
Anonymous2006-01-24 2:16
die horribly
Name:
Anonymous2006-01-25 8:55
1 / 0 = ∞ you mofos; however, 10²³ is not a better approximation than 2. Oh and n MOD 0 = n.
Name:
Anonymous2006-01-25 11:11
>>51 >>53
how many times do i have to say this. "in a zero ring fuckers"
Name:
Anonymous2006-01-25 12:36
>>53
please explain exactly how 1/0 would be infinity.
Name:
Anonymous2006-01-25 13:22
infinite 0s fit into 1, which is false as infinite 0s = 0, but some people just don't realise that 0 isn't a real number as they are inferior and stupid
Name:
Anonymous2006-01-25 13:42 (sage)
>>56
Some people also have a social life and don't spend time caring about such worthless shit. But you wouldn't know that, would you...
Name:
Anonymous2006-01-25 19:17
>>55
Closure, walking an infinitely small amount towards both sides, and common sense.
>>56
Didn't know it was not a real number. 0 Є R IIRC.
Name:
Anonymous2006-01-25 20:23
>>58
0.1*2 = 0.2
0.1*3 = 0.3
0.1*4 = 0.4 etc etc..
no matter how many time you multiply 0.1 the next number is always higher, so if you multiply it by infinity it becomes infinity
0*2 = 0
0*3 = 0
etc..
0*infinity = 0
0 just doesn't share the same properties as other numbers
Jesus why do you fags keep bringing infinity into this? go back to high school and finish that math first lol
Name:
Anonymous2006-01-26 8:35
>>59
You lost, I meant approximation like 1/n=x; x grows as you approach zero.
Name:
Anonymous2006-01-26 9:53
>>60
look you idiot. take a 0 ring. consiting on only 0. it's additive identiy is 0 in the ring. and mutiplicative identity is 0 in the ring.
so we have 0/0 = 0 in the 0 ring. we aren't talking in any other ring. so fuck off
Name:
d2006-01-26 10:28
The zero ring may, or may not, exist; depending on your lecturer's taste.
In any case, this is all useless trivia, hence there are really no standard definition.
Name:
Anonymous2006-01-26 13:40
>>64
of course it exists {0} with addition 0+0=0 multiplication 0x0=0
additive identity 0, 0+0 = 0, additive inverse 0 of 0 , 0 + 0 = 0 and then you have the commutativity and distributivity
0+(0+0) = (0+0)+0
0(0+0)=0x0 +0x0=(0+0)0
Name:
Anonymous2006-01-26 15:01
>>65
In other words, it's completely useless except for fuckwits who want to be able to divide by 0 and be "right".
Name:
Anonymous2006-01-26 15:11
>>65
No, sometimes the condition is that 0=1, ala rings. This axiom makes the zero ring impossible to construct. The trivial ring then becomes ({0,1),+,*).
lim(x/a,a,0) = inf, though, where that means the limit as a goes to zero.
Name:
Anonymous2006-01-29 5:07
>>82
inf. * 0 = 0, if you have 0 infinities then you have 0
infinite 0s makes 0
x must be 0
Name:
Anonymous2006-01-29 6:19 (sage)
>>82
a/x as x->0 does not have a limit >>83
infinity isn't a real number and as such those algebraic expressions are meaningless
Name:
Anonymous2006-01-29 6:35 (sage)
Does anyone notice that three people seem to have been repeating the same fucking point over and over and over and over again while proving only that they are fuckwits, talking about a subject no one cares about, and that has (ironically) ZERO utility?
Fucking retards.
Name:
d2006-01-29 7:02 (sage)
>>85 Well maths is pretty boring. Pointing out little flaws in people's mathematical naivete is pretty much the highlight of my day.
>>88
Well here's a subtle hint. If you see a girl (they're the things with breasts and nice asses), never EVER talk about ANYTHING related to the zero ring.
Name:
Anonymous2006-01-29 9:14
I'm not the Zero Ring Guy. And I might as well talk about the zero ring since there are plenty of attractive females maths students. around here.
Name:
Anonymous2006-01-29 12:15
>>90
Lies! They're men so desperate to get laid SOME way that they dress up as women.
>>113
Yes, it is in fact Defined as all things that are Undefined, this means it is beyond our comprehension at this point. >>111
I have to agree with good old Shaquille here. >>107
\Omega,
\O,
/0,
Hmm, you say they use (divide by/over) Zero(or the term Omega which I believe is "The End"?) to define INFINITY?
Well, I guess you could say that is what infinity IS. So it would only make sense. >>102
None of them are counted, but the Real number stands as the index when you /0, so as while underneath those infinites are an infinite amount of zeros, it is a straight line of them down that follows on the number path or ring or whatever MAKING it a field, though a completely one dimensional field(infinity rests behind them remember, each number in the count,there is no infinity real so there cannot be an array containing infinity with the index size of infinity) meaning that you now have two types of numbers. Those that are just numbers and those that have an array (or a ray of infinite zeroes under each number) of infinity, a term that could be considered xi, but i is already used for imaginaries, these are not imaginary, those zeroes are there, they're just zeroes, because they are undefined.
Hmm, undefined wait isn't that what they were already defined as, time paradox or what not? Not so, you just use what zionist used or use xu instead, to stand for infinite undefined zeroes.
So, 3/0=3u, maybe this is what the R is these people are talking about, but I have no idea what it really is so I won't comment >>99
The problem is showing that the number is plain or contains infinity, while you're busy in rings and fields and various other dimensions that do not include the dimension infinity rests in and I guess that it should be stated that infinity exists in the 4th dimension, time, as it IS time in a literal sense, unless of course you're DIO and have been around long enough (and gained the help of KAAZ) to figure out how to use /0 or Xu to defined the undefined values, or maybe empower all the forms of math to include infinity aka time on the numbers, to have true control over them and be able to stop them.
The name of the function? Why the name KAAZ took when he granted his spirit as a stand to dio, in a vain hope to get revenge on Joseph for sending him into space where he could not use his physical body.
za warudo.
Name:
d2006-02-20 16:08
>>114
no, cantor proved that there is no cardinal number (aka "the infinities") between |X| and |P(X)|. |N| is the smallest infinity (each subset of N with an upper bound is finite), hence...
there is a natural bijection between the cardinal numbers and the natural numbers (f(1)=|N|, f(n)=|P(f(n-1))|), therefore that they are countable. QED.
don't they teach you this shit as an introduction to topology?
oh wait, you're 14 right?
sigh
Name:
Anonymous2006-02-21 16:19
Include the first dimension in your numbers to include the fourth?
Or don't it's fine by me.
>>24
The real numbers are defined as the set of limits of all converging infinite sequences of rational numbers, which are in turn defined as the ratio of two integers m and n, where n is nonzero (ie m/n). Thus, let
a_n = m/n, where m=0, n=1. 0,1 are in the integer set.
Then the limit of a_n as n->infinity = 0. Thus 0 is in the real numbers by definition because it has just been demonstrated that it is the limit of an infinite sequence of rational numbers.
QEDw4ch?
Name:
Anonymous2006-02-23 13:07
no, the real numbers are defined as the set of _equivalence classes_ of cauchy sequences where a_n = b_n if lim a_n = lim b_n as n -> inf
if you're going to be a smartass then at least get that right
Even though dividing by zero can give different results depending on the situation. I like to to be able to do it. Specially when I code I apply division by zero for some special tricks.
What I usualy regard division by zero is a not actually a division by zero but a number that is going towards zero and from the pattern of results aquired you approximate what a division by zero would yeild. No fuss, just some general logical acceptance.
Name:
Anonymous2006-02-27 19:51
Zero division is possible, it only depends on how you can store +INF and -INF
Name:
Anonymous2006-04-14 22:38
Dividing by zero - it builds character
GET
Name:
Anonymous2006-04-15 0:31
people throughout this thread who think infinity is a number are retarded.
Name:
Anonymous2006-04-15 4:11
Chuck Norris can't be divided By 0
Chuck Norris/0 = Chuck Norris
Name:
Anonymous2006-04-15 11:28
>>125
OH funny I had thought it WAS in fact a number
Obviously it must be a letter, the highest letter you can spam up to on world4ch, thank you for the clear information anonymous.
Name:
Anonymous2006-04-15 12:42
>>127
it's not a number, its a trend. it lacks finite-ness. it is more than any finite number. that is why it is infinite.
Name:
Anonymous2006-04-15 18:32 (sage)
its still a fucking number, what does that trend in fact represent again?
exactly
Name:
Anonymous2006-04-15 20:09 (sage)
hi guys
lets be retarded and argue definitions
Name:
Anonymous2006-04-16 0:07
>>129
youre pretty thick. by definition, it is not a number. so no, it is not a number, and it never was.
>>133
alright, look. if it were a number, you could add one to it to get a larger number, and that would be the new infinity, and the process could be repeated. however, arithmetic with infinity works like this
infinity + 1 = infinity
if you assume it is a number, shitloads of absurdities arise.
you can keep saying its a number all you want, but it's not, and anyone who knows shitfuck about it will know you're wrong.
Name:
Anonymous2006-04-16 19:05
What I wonder is, why does my FPU differentiate between ±NaN (Not a Number) and ±INF (Infinity)?
Name:
Anonymous2006-04-16 20:07
>>135
Alrightly, look, if it weren't a number, WHAT THE FUCK DOES IT REPRESENT, WHAT DOES IT CONSIST OF? LETTERS? TURTLES? DELICIOUS FUCKING CAKE?
NO, ITS FUCKING A NUMBER
Name:
Anonymous2006-04-16 20:15 (sage)
>>137
It represents a value larger than any real number, dumbdick.
no. in the extended real numbers, you just add two points which aren't reals, and order them to be either greater or less than every real and then denote them using symbols -inf and +inf.
Still wondering why is Infinite different to Not-A-Number in my FPU. It means it thinks Infinite is a number.
Name:
Anonymous2006-04-17 19:35 (sage)
>>144
No, it just means the people who made the standard thought it would be a good idea to have division by zero give a distinct result.
PROTIP: Math is defined by mathematicians, not computer standards committees.
Name:
Anonymous2006-04-17 20:29
no. in the extended real numbers, you just add two points which aren't reals, and order them to be either greater or less than every real and then denote them using symbols -inf and +inf.
142
Anonymous at 17 Apr 2006: 05:49
the fact is, >>140 will never be math champion.
144
Anonymous at 17 Apr 2006: 18:29
Still wondering why is Infinite different to Not-A-Number in my FPU. It means it thinks Infinite is a number.
145 (sage)
Anonymous at 17 Apr 2006: 19:35
>>144
No, it just means the people who made the standard thought it would be a good idea to have division by zero give a distinct result.
PROTIP: Math is defined by mathematicians, not comput
Which is exactly why we do not rely upon programmers to define math. Programmers set convenient tricks to make writing programs easier when dealing with special cases, like division by zero and infinities.
THESE DO NOT CORRESPOND TO THE REALITIES OF MATHEMATICS.
I could write a program that says 42/0 = apple, and you fuckers would think that made it true.
Division by zero is indeterminate, except in special cases. Infinity is not a number in the regular meaning of 'number.'
∞ ∉ ℝ
FAIL
Name:
Anonymous2006-05-07 5:57
everyone here fails for not knowing math beyond calc 1. a / 0 = ∞ on the Riemann sphere (i.e. CPL).
Name:
Anonymous2006-05-07 20:25 (sage)
>>175
"a / 0 = ∞ on the Riemann sphere"
which is a special case.
Name:
Anonymous2006-05-08 2:49
no, it's not.
Name:
Anonymous2006-05-10 17:07
>>25
(and all others)
There is no such thing as "division" in the zero ring (or the trivial ring)
Rings are not required to have the property that every element has a multiplicative inverse. Therefore division is not defined for rings.
Otherwise we're talking about groups but even then division isn't defined because multiplication in groups isn't necessarily commutative so there really isn't any definable division "operator".
So it requires a FIELD to have division, and fields require additive identity != multiplicative identity, which makes the trivial ring {0} usless.
So division by the additive identity is never possible. QED
Name:
Anonymous2006-05-10 18:54
a / 0 = ∞ in the zero ring, but not the Riemann sphere.
Name:
Anonymous2006-05-10 20:10
6 IS CONGRUENT TO 12 MOD 3
3 IS CONGRUENT TO 0 MOD 3
DIVIDE BOTH SIDES BY 0
2 IS CONGRUENT TO 6 MOD 1
Name:
Anonymous2008-06-29 4:10
On a graph, yes.
Name:
Anonymous2008-07-01 0:53
>>178
the zero ring {0} can be thought of as a field, where {0} is both the additive and multiplicative identity, and its own additive and multiplicative inverse, in which case 0/0 = 0.
although 0/0 is traditionally considered an indeterminant, it is colloquially treated as equal to 0 in most cases. similarly to how n/0 = \infty when n is nonzero, except in a few cases where paradoxes can occur which have to be specially dealt with.
>>184
But an infinite quantity of 0 can't fill 1. That's why it's more accurate to say it's UNDEFINED.
Name:
Anonymous2008-07-03 4:52
>>185
An infinite quantity of man-meat fills your sphincter every night.
Name:
Anonymous2008-07-03 5:54
Jeepers, that man-meat would be enough to propel semen to the speed of light, then.
Name:
Anonymous2008-07-03 9:03
1/0 is simply a line with no slope. It has always been defined as such in basic Algebra.
Name:
Anonymous2008-07-03 17:32
it's safe to say that the limit of 1/x as x approaches zero is infinity, but since infinity is just a concept there is no such thing as 1/0, since 1/0 is greater than infinity.
Name:
Anonymous2008-07-04 5:47
>>188
basic algebra defines a lot of shit out of convenience because actually explaining it would involve shit thats too complicated to comprehend for an 8th grader.
also, 1/0 is not a line, no matter what your graphing calculator wants to show you.
Name:
Anonymous2008-07-04 10:32
How is it not a line?
Name:
Anonymous2008-07-05 7:43
>>191
how CAN it be a line? its one number divided by another number... a line is a set of solutions to a linear equation.
Name:
Anonymous2008-07-06 12:27
er, X/0.
Name:
Anonymous2008-07-08 16:08
One thing:
0 is a number, a quantity. What you conclude of it is other thing. 'Nothing' isn't a Mathematical term.
>>196
That's a Danish/Norwegian slashed O, not the empty set. The empty set is ∅.
And yes, they are distinct.
>>197 Null set was once a common synonym for "empty set," but this usage should be avoided because "null set" is now a technical term in measure theory.