infinity

ArielGenesis

if

a/x*x = a

then if x =0

a/0*0 = a

but they say that:

n *0 = 0

and when n =a/0

so that

a/0*0 = 0

instead of a

xJuggleboy

a/0 does not = 0

anything/0 is undefined

lawtonfogle

do you know that long ago when some one asked what 5-6 was, he was told undefined(ok not exactly that, but something that meant impossible)

sooner to present day, some was told that (-4)^.5 (that is square root of -4 without using square root sign) was impossible, untill someone thought outside the box and cam up with imaginary numbers.

time to do that again

nnnnnnnn

5*0 = 4*0

If you can divide by zero, then the zeros cancel and 5 = 4 and you end up with a number system with only 1 element. Its not so much impossible to come up with a system that allows you to divide by zero, its that it would be limiting rather that useful..

Hurkyl

And they were right.

And they were right.


It's not a matter of "thinking outside the box" -- it's a matter of definition. Long ago, people used a number system that consisted only of positive numbers. Thus, it is correct that 5-6 was undefined. And it's still undefined in that number system. The fact we invented negative numbers doesn't change that fact.

Similarly for your next example.


The problem with wanting to invent division by zero is this:

0 = 0*x - 0*x = (0 + 0)*x - 0*x = (0*x + 0*x) - 0*x = 0*x + (0*x - 0*X) = 0*x + 0 = 0*x

Each of the steps in this equation is something that is extremely desirable for a number system to have. Here, I've used:
Subtracting something from itself yields zero.
Adding zero to something leaves it unchanged.
Multiplication distributes over addition
Addition is associative.

Thus, anything that has these nice properties also has the property that 0*x = 0 for all x.

Thus, if we wanted to define division by zero, we must have:

0*x = 0 = 0*y
Therefore x = y. (Dividing by zero)

In other words, it would require every number to be equal to every other number. That's not a very interesting number system now, is it?

In order to have a useful division by zero, one has to give up at least one of the properties that makes a number system useful.

ArielGenesis

so hurky you mean that the number system where every number to be equal to every other number isn't interesting.

and by the way i'm confuse wether 1/0 = undefined or infinity

if i asked u that wether

1/0 < 2/0

if yes then 1/0 suppose to be a form of constant

quark

It is just undefined(not infinity).

Let us say, 1/0 = infinity. As infinity still holds some mathematical value 0*infinity = 0, thus 1 = 0.

When a teacher was explaining his elementary school students about dividing a number with same number and always getting the value 1, he took an example of distributing 5 apples among 5 students, 4 apples among 4 students etc.

A boy stood up and asked that if there were no apples and they were distributed to nobody, still everybody would get 1 each?

The boy asking about division by zero was the great Srinivasa Ramanujam and he was 8 year old that time.

quark

I am sorry. On a second thought, my explanation seems to be wrong for, 1/infinity = 0 and so if infinity*0 = 0 then 1 = 0.

You just consider 1/0 is undefinied.

ArielGenesis

so if we have a curve where y= 1/x and at a point where x=0, was taught that y = infinity instead of undefined. infinity point on cartesian plane is somewhere imaginary. while undefine should be nowhere or does not exist.

Icebreaker

y = infinity means y is undefined.

<<<GUILLE>>>

Does someone know which are the different types of undefinitions in math?

and esclusively, what is zero times infinite?

nnnnnnnn

when x approaches 0, y approaches +infinity or -infinity depending on direction... that's one of the reasons 1/0 is undefined.

there is no point at x= 0, it is untrue that "there is an imaginary point...", it does not exist.

nnnnnnnn

this doesnt work becaus infinity/infinity does not equal 1, it is undefined.

for <<<GUILLE>>>, 0*infinity = 0

<<<GUILLE>>>

thanks.

and zero/infinity?

and infinity/zero?

nnnnnnnn

zero/infinity = 0 ...anything not (+,-) infinity is zero when divided by (+,-) infinity (this may actually be undefined, but its limit is 0)

infinity/zero DNE

<<<GUILLE>>>

thanks again.

one more, what is -infinite+infinite?

HallsofIvy

There are not "different kinds" of "undefined"s. "Undefined" means exactly that: there is no definition for that combination of symbols- it makes no sense. As far as the real numbers are concerned, any formula involving "infinity" is "undefined" because infinity itself is undefined. Asking "what is 0/infinity" is exactly the same as asking "what is 0/green beans?".