I've been debating this with my friends... so, if you give the operation (for example) 10 / 0, some people say one, some people say ERROR (autodestruction)... I'd rather think it would give 10... I mean, basically, 0 is nothing, right? so 10 divided by nothing equals 10, since it is not divided... same goes for all other numbers... Of course, it all depends on how you see it... if you see it as 10 from 0, 0 parts of 10, 10 divided by 0... ( i know some points are confusing, but I still want to hear your opinions about the main idea xD) Discuss?
It really depends what kind of answer you are looking but in general that is considered undefined or infinity.
Bizarro "i" is defined as the square root of negative one. And the answer like i already said is either infinity or undefined depending on the equation your are using.
bizarro is correct, the solution of x/0 (where x is not 0) could be technically considered as another imaginary number just like i, just not the same as i
No any number divided by zero is a real number or concept because infinity is a concept not a number and every now and then something divided by zero can infact create a number but these are few and far between.
i is defined differently depending on the community. Maybe in Strict Mathematics, it's defined as the square root of a negative number, but in Principles of Logic, it's defined as any imaginary number. X / 0 cannot equal infinity. It doesn't make sense. You cannot fit a whole into a nothing. Let alone do it endlessly. If you can offer me one instance where something divided by zero will create a number, though, I will completely concede my position. Bird, I realize that the square root of a negative number has nothing to do with this. I was merely using it to further illustrate my point.
The reason for the infinity used to mark that is infity is undefined so they use it to represent the answer to x/0. It is a shorter way to write undifined
it is difficult to play with things that can create infinity or zero in mathmatics. but an example could be (even though something tells me you wont like this answer) the limit as x approaches 0 of (7x)/(sin(x)) (sin(0) btw is zero) would be 7 by using l'hopitals rule. As for zero divided by a number equaling infinity if you graphed the equation y=(x/0) you have an equation with a slope of infinity because you would have a vertical line for your graph so x wouldnt need to change at all before y equals infinity.
the reason why infinity is use is because the solution of x/y tends to infinity as y tends to 0, but when y becomes 0, x/y becomes undefined, infinity is used as the solution of x/0 in computer science (which i am studying at university) because it's a applied subject, where practical application is more useful than theoretical correctness. for all purposes of actual practical usage, infinity does the job. as for why the solution of x/0 could be considered a imaginary number, it is because there doesn't exist a real number n for which n*0=x (x=/=0), just like there doesn't exist a real number i such that i*i < 0. but we can define imaginary number to be solutions that satisfy such equations, just like i. hence they are called imaginary numbers.
Reacker while i would agree with you for the most part i would say a number divided by zero is real (even if we dont quite understand it) becuase we can still describe what happens in that situation were as with imaginary numbers we cant even do that much. (as always take everything i post with a grain of salt because while math is defintely my strong point i by no means know enough to talk in real depth about this disscussion)
i think it might be easier to understand using functions. a function is a special relationship were each member of the domain can associate with (be mapped onto) at most one member of the co-domain. a injective function is one where no two values from the domain maps onto a same value in the co-domain. a surjective function is one where every value in the co-domain is mapped onto by some value in the domain a bijective function is one that's both injective and surjective. only bijective functions has proper inverse functions a well defined function is one were every member of the domain is mapped onto some member of the co-domain in general multiplication by x where x does not equal to zero is a bijective function (meaning for all numbers n, x*n is unique (injective), and for all numbers m there exist a number y such that m=x*y (surjective)) since it's a bijective function, it must have a inverse function and that function is division by x. however multiplication by 0 is not a bijective function, every value from its domain is mapped onto 0 and no value maps to any other number. this means the multiplication by 0 does not have a inverse function. division by 0 is not even a function as it maps 0 to every number and maps every other number apart from 0 to absolutely nothing. so it's neither proper nor well defined that is why division by 0 produces all these problems similarly raising to the power of 2 is not a bijective function, because it maps both the +ve and the -ve of a number to the same value in the co-domain (not injective) and it maps nothing to a -ve value. that's why taking the square root of a -ve number is undefined, because it maps -ve values to absolutely nothing, exactly the same way division by 0 maps every other number apart from 0 to absolutely nothing. that's why we can invent imaginary numbers for both of them and why we can't for 0/0
ok heres a simple explanation... if you divide 10 by zero, it means you're dividing something to zero right? so you're looking for results right? soooo.... if you divide something to zero, means that you're dividing something to nothing, thus.... you have no results.... thus its undefined because you have nothing, no results......... got it??? oh and i think "i" is not infinity: its imaginary...
Right... Well, I guess my teachers don't know much after all ^_^ Most times I ask a question like this they can't answer appropriately =X Thanks for the explanations... but, if we go by your rules, ursa, then if we do 10 / 1 it would mean we divide it to one, so it should give 1? but that's not true, cuz it gives 10... Unless that was a casual explanation that only refers to zero and doesn't apply to others?
