What is this wack not defined bullshit? Why does it appear so many times in mathematics and what does it actually represent?
What is this wack not defined bullshit? Why does it appear so many times in mathematics and what does it actually represent?
What is this wack not defined bullshit? Why does it appear so many times in mathematics and what does it actually represent?
consider newton's law of gravity where the denominator is the square of the distance between two celestial bodies of mass.. if the distance between two celestial bodies were zero, meaning joined center to center as described in Plato's Timaeus, then Newton's law of gravity would be undefined, implausible, and outright false.. a new theory would be required, such as magnetism.
Try defining it.
As in wheels or meadows?
>Try defining it.
It limits to infinity, which is exactly what it is.
"ThE ArE nO ReAL InFiNITIES...."
Math disagrees, so, uh... how about shutting the frick up?
It is not "infinite", it's a contradiction. This has been explained by several posts. You can't divide or separate something by not dividing it. You are treating "0" as a regular number when it absolutely is not.
My dear blatantly obvious troll, I have here a bond for 7 apples and I wish you purchase my -7 apples for its face value. Tee hee.
>It is not "infinite", it's a contradiction. This has been explained by several posts. You can't divide or separate something by not dividing it. You are treating "0" as a regular number when it absolutely is not.
No one said it's a regular number, Boomer
Reply did, moron. You must be another bot
You don't know what words mean. Sucks to suck.
>You don't know what words mean. Sucks to suck.
Find God, my child.
>it's a contradiction
Kind of like how all the energy & matter in the Universe sum to 0 but are infinite.
Stfu
renorlamination
I'm not a troll. there cannot possibly be such a thing as a "negative amount", which is why its idea leads to a logical contradiction that forces mathematicians to cop out by declaring it to be "undefined". x/0 = inf.
the problem is the notion of "amount", in reality there is no such thing positive or negative
how do you measure temperature below 0?
You can't, the concept of "measure" is meaningless
That's just silly
With a thermometer.
but how do you mark said thermometer?
I don't, I just read it.
oh so your solution is to use something less precise
less precise than what? I can buy a thermometer as precise as is needed for any purpose.
and how is it marked on quantities below 0?
with negative numbers, unless it's using kelvin
it's the exact opposite. everything is just plus and minus interacting/vibrating on various scales. reality is a hologram and penis in vegana is its pattern.
okay, but why not negative infinity?
because the inputs to 1/x are negative in that case. learn what limits are
Noone says that. What we are telling you is that infinity is not a number, you stupid frick. You can't combine two numbers in any way to get infinity.
Off yerself.
>I hereby define the quotient of a/0 as ad or:
>ad≡a÷0
>The sum of all numbers of the form ad (for example 7d or 142857d will henceforth be known as D or "Dumb Numbers".)
Hope you guys are happy, now.
Now protect your new brand. You need a published paper to push it properly.
It is a logical contradiction "to separate by not separating".
That is as simple as it is possible to frame the answer without going into anything else.
Shouldn't dividing by 0 give you the number?
5 divided by 0.
Means take 5 and divide it 0 times
You are left with 5.
that is what happens when you divide by 1
as the denominator approaches zero the quotient approaches infinity
You already have that case for division, though, when you are dividing by 1. 5/1 is 5. The issue is thinking about "0" in terms of a "something" to act on something else with, but in fact it is not a "something" and there is no relationship between something and nothing.
5/0 in that case, perhaps more accurately to the totality of what it means, "what is the relationship between 5 and zero". That answer is "none whatsoever", and so it is undefined. To "act with" nothing, too, is a contradiction. One cannot "separate five without separating five" for example.
I'm trying to give simple analogies because anyone asking is probably not going to appreciate latex or jargon. If someone can improve upon my analogies please do so.
Ok, 9 divided by 3, says cut 9 into 3 equal parts.
5 divided by 2 says cut 5 into 2 equal parts, 2.5 and 2.5
5 divided by 1, cut 5 into 1 equal part. So thats 5. Or how many 1's are in 5, that method also for the other examples.
5 divided by 0, how many times does 0 go into 5, we see it's a meaningless nonsensical unstartable problem, 5 divided 0 times, 5 cut into 0 equal pieces,
no, 9 divided by 3 says 1 third of 9
You have five apples and need to give them to zero children. Since there are no children, you still have five apples. Did the division happen? If it didn't happen then it's not defined.
It did, it was divided by you
Correct for natural numbers
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.56.3442&rep=rep1&type=pdf
Brainlet.
The inverse operation between multiplication and division.
4 x 2 = 8
8 / 2 = 4
15 x 4 = 60
60 / 4 = 15
5 x 5 = 25
25 / 5 = 5
This rule does not apply when multiplying by 0.
4 x 0 = 0
0 / 0 =/= 4
Think of dividing as splitting something equally into groups of x.
So like splitting 5 into 1 group leaves 5 elements per group, splitting 5 into 2 groups leaves 2.5 elements per group.
So what does splitting something into zero groups mean then? How do you split something until there's no groups?
Maybe it means you just keep splitting, creating infinitely small numbers for infinitely many splittings.
If there is an answer it has to equal 5 if multiplied by zero, but that makes no sense as anything times zero is zero.
>thehindu.com
Not a peer reviewed source. Try again.
It's a pooer reviewed source, even better. Try again.
>What is this wack not defined bullshit?
Because math should stay applicable to the real world?
We dont define it because it would break all of math and not help anyone.
You define a function over some objects in either of two ways, telling one by one wich elements goes to each number (or whatever the elements of the set are) or you give a general rule that tells you how to find wich number belong to each particular element. Not defined means that a given general rule it doesn't asign any value to a certain element of the set. For example the function 1/x is literally and equivalent to "assign to A the number that multiplied by A equals 1". You take values of lots of numbers and plot the function. When substituting A by 0 the rule tells you to "assign to 0 the number wich multiplied by 0 gives 1". There exist no such a number so the rule doesn't assign any value to 0 so it is not defined on 0. Thats pretty much it
it is only not defined, because the result could be infinity or minus infinity. whenever something "isn't defined", it actually means there is a mistake in the framework. the easy and clear to see solution is that negative numbers cannot exist and the result is therefore infinity.
>give me negative 7 apples please
moronic nonsense. just because it is comically easy to use negative numbers does not mean that they make *any* sense whatsoever.
Apparently it's hbar/2 divided by zero in quantum mechanics is equal to infinity in the context of stationary states, if what I heard from this professor's lecture on YouTube is correct.
Why do brainlets have so much trouble with this?
In ordinary english language a word "xobgluk" is not defined.
It allows you to create a product, like, say, some kind
of oat yoghurt or other vegan crap, and give it the name
xobgluk, so that for all time thereafter, there will be a definition
of a xobgluk. So it has been defined, and is no longer undefined.
Here is the shocker: it is exactly the same in mathematics.
If someone says "we do not define 1/0", it means that no it
becomes a free for all to invent something new and call it 1/0.
At which point the brainlets bawl their eyes out and go all
"oh no, we cannot deal with this freedom to define 1/0 to
be anything we want, please help us /sci".
Pathetic.
It just doesn't have an answer
0 shouldnt be considered as a number in the first place
What's a+-a?
nothing
and what's 1/(a+-a)?
1
which would imply (a+-a)=1
>imply
moron
?, going by the traditionally accepted laws regarding natural and negative numbers, that is indeed what it would imply
this is exactly the problem of such logical unfoldings overly focused on short-term utility
there are infinite ways axioms can be defined and all of them have a wide range of benefits and drawbacks
https://ee.usc.edu/stochastic-nets/docs/divide-by-zero.pdf
It's an operation not defined IN THE REALS, discussing the philosophy of whether you can divide by zero reeks of schoolboy math, in reality the extended reals do have a solution for this (+∞) and is present in just about every real analysis text.
Undefined doesn't mean paradoxical or impossible or whatever, it's merely an expression to which no value is assigned, for example in N, 3-4 is undefined, in R, sqrt-1 is undefined, etc.
>what does it actually represent?
[math] left( begin{matrix} -c^2&0&0&0\0&1&0&0\0&0&1&0\0&0&0&1end{matrix} right ) neq left( begin{matrix} -c^2&0&0&0&0\0&1&0&0&0\0&0&1&0&0\0&0&0&1&0\0&0&0&0&0end{matrix} right ) [/math]
Imo it's because our mathematical division is fundamentally flawed and illogical
If it was realized properly it would represent how many times whole number got "sliced" into parts
Instead it skips it to "into how many parts it got sliced" which is fricking moronic when you think about it and shouldn't be called division at all
So for example if used my style of division it would be:
10/0=10
10/1=5
10/2=2,5
See how much better it is?
10/2 = 3.33333.... in that case, no? but I like the idea.
Yeah my bad it's 3.333...Same as normal just using one number less
this is just normal division by x but by x+1 instead, it loses a bunch of useful properties e.g. a/(-b) =/= -(a/b), and also doesnt solve the issue at hand (what is 10/-1)
"Math" is playing games with sets of rules. The rules are arbitrary, you invent new rules and see what kinds of games emerge from your new ruleset. You can define division by zero to mean something, then do math like that.
When they say it isn't defined, they mean it's not defined in the ruleset most people customarily use.
>Why does it appear so many times in mathematics and what does it actually represent?
?????
>Not defined
>So by definition it NEVER appears in mathematics
>...
>why does it appear so often guys???
have a nice day
If I put a square peg into a round hole, is the result undefinable?
We want multiplicative inverses to have certain properties that reflect our empirical experience with fractions.
Assuming that zero has a multiplicative inverse (which amounts to saying that "1/0" exists, which amounts to saying you can divide by zero) leads to obvious contradictions, so we can't have that.
Given any nonzero number x, its inverse is 1/x and you know that x(1/x)= x/x = 1. So if we asusme that division by zero is possible, it means we are looking for a number y = 1/0 such that the product of zero and y is equal to 1: 0y = 1. Because of the distributive property, this is impossible, since any number multiplied by zero equals zero. Here is the proof:
Given any real number a, we have:
0a = (0 + 0)a = 0a + 0a
Subtract 0a from both sides and you get:
0 = 0a
QED.
Therefore there is no number y such that 0y = 1, so zero has no inverse, so you can't divide by zero, end of the story.
Probably the best 3 answers in terms of brevity, accuracy, and scope.
HOWEVER! let's have some fun.
Mathematics is a broad field of many subfields, and some of them utilize different assumptions. I am freely admitting to flying the coop. We're going to go off into the rails, out to lunch, flying over the cuckoo's nest. In spaces or framing other than our standard algebra. This is kind of impossible generally anyway because most people can barely get the standard algebra under their control.
Further reading in general, https://en.wikipedia.org/wiki/Algebraic_structure
Moving along quickly, there exists what's called "unconventional division by zero", where one can have an algebraic system and topology where division by zero can be defined. Many people including Euler had different ideas on this, and Euler rightly points out zero could be doable if it is the reciprocal of infinity. https://www.semanticscholar.org/paper/On-Unconventional-Division-by-Zero-Czajko/736417e4606bde3f67e4341f72824dd9c5a8ceb8
The linked paper in effect explains how, as an inverse of infinity, you get Euclidean representations as this anon shows.
which would represent easily something like two spheres (say, Quaternions for example) and the zero is the axis of rotation. 0p/0q where p/q can be our "views" or reference frame of viewing the object.
So suppose a contrast, then. Complex numbers give us a rotation around an axis on a Euclidean plane, and Quaternions give us figures we can plot as rotational vectors in a matrix and are also homeomorphic. Why not, then, plot the spatial reference frame? After all two opposing reference frames would have inverse limits as you see normally with 1/x. Dividing one reference frame by another's zero, then, is entirely possible (interspatial division).
Is this useful? I haven't the fricking foggiest because I postulated this out of boredom only to discover some bastard published it 4 years ago. FML.
So anyway a possible way you could define it would be along which of the two possible axis on a standard euclidean plane your reference frame would fall on. So 1/0p or 1/0q would have opposite results in terms of how the limit is approached.
>0
There is no such thing
Division doesn't really exist. "Divide by x" is just a pointer to "multiply by the multiplicative inverse of x." Zero doesn't have a multiplicative inverse. Multiplication is fake anyway.
how do you define something as "not defined?"
OK. SO JUST TAKE 3 THINGS OK, AND SPLIT THEM INTO NO GROUPS AT ALL. NOW.
TELL ME EXACTLY HOW MUCH THINGS ARE IN EACH GROUP-WHAT DO YOU MEAN THERE AREN'T ANY GROUPS-TELL ME HOW MANY THINGS ARE IN EACH GROUP RIGHT NOW