Can someone give me a full explanation on how Division by zero is undefined? Thanks.?

Question

Thanks everyone! You all helped me out alot!

Answer 1

Hi:

The reason you can't divide by zero is this

what is division?

it one of two answers

repeated subtraction or multiplication in reverse

Okay! here how to think it :

divide 9/ 3 = 3 because 3 *3 = 9

or 9-3 =6 than subtract 6 again by three ( 6-3= 3) than subtract 3 by three again ( 3-3=0) by counting the number of subtractions which is 3 we find that 3*3= 9 or 3+3+3 = 9 So that 9/3 is proven to equal 3. Do the math youself

Okay now to try to divided by 0? Do the division for yourself

10/0 =?

10-0= 10 try again 10 -0 =10 you never can bring 10 (in this case) down to value other than 10 no matter how time you subtracting it by zero . So the number of subtraction will become infinite

and the number of solution is infinte when multiplying by zero because any number time zero equal zero so that dividing by zero has a infinite number of soultion thus dividing by zero is a undefine operation. There was one expection to this when you divide 0 by 0 it equals 1.

Do the math yourself

Answer 2

If you know that 6/3 = 2 is really just a different way to write 6 = 3*2, then you can do the same thing with something divided by 0.

3/0 = x because we're not sure what this should equal.
So if we rewrite the division as a multiplication problem we get
3 = 0*x
So now looking at this equation try to find a number that will multiply times 0 to get three, since there is no number that will fill in for x.

So division by zero has become undefined.

Hope this makes sense.

Answer 3

So, I see a lot of practical answers here, and that's good. Most of these ideas deal essentially with this idea:

limit of 1/x as x->0

As most people know this is undefined. It seems to me, however, that this isn't really so much a property of zero so much as the non-closure of the real numbers under division.

Confusing? Well, let me illuminate the meaning of that. Essentially, every time you divide by a real number that isn't zero, you get another real number back. That means that for every member of the real number group, you get another member of that group if you divide. Now, for multiplication, addition, and subtraction, the group we just mentioned is closed. IE: No matter what you do with these operations, you'll always get a real number back.

So... we know that zero is a part of the real numbers, yet when we divide by it we can't find a number in the real numbers that satisfy the equation. Hence we called it "undefined". Well, rather, most people call it infinity.

Infinity is not part of the real number line. It *is* part of the extended real number line. It still doesn't solve our situation (we've replaced undefined with infinity) but it does give us an idea of what happens. Unbounded would probably be a more descriptive word. So, in other words, as you divide by zero, you create an unbounded quantity.

So, it's undefined because the operation of dividing by zero takes you out of the group of real numbers, and hence can't be used in normal algebraic considerations.

If you want a similar issue, try dividing two vectors. We don't even know what that would be. (Multiplication works nicely though, but we have to define how we're gonna multiply, so even that's tricky).

Answer 4

thats not easy because definitions are where we start

we define something and after that we can use it

it is sort of like trying to explain WHY the word "cat" is defined as that furry animal with the whiskers, its not really a why question

now, you could ask, how that came to be defined that way, or what is the history of that word

mathmatics is all made up
lots of it applies directly or indirectly to the real world, but the math is just something we invented to help us model things

we invented the term "division" and it does mean to divide
the idea that if you had 100 cows, and you DIVIDE them up between your 10 kids, each kid gets 10 cows

100 divided by 10 = 10

what if you decided to divide your cows up between your 1 kid
that means 100 divided by 1 = 100, and clearly the kid gets all the cows

now, what if you had no kids, and you wanted to divide your cows up amongst no kids

100 divided by 0 does not have a defined meaning, it is not possible to do, it makes no sense, the math does not treat it

you can't split your 10 acorns into zero piles, it has to be in at least one pile

we made up the definition of "divide" and we made up how we would arithmetic

we made up zero as a number and the math does not give an answer to anything divided by zero

maybe that helps
maybe it doesn't
good luck

Answer 5

Divide 90 marbles into zero groups... it's not possible. You can divide it into 1 group (90) or 2 groups (45) or 3 groups (30) but can you divide it into 0 groups? No. You'd have to get rid of all the marbles, but they have to go somewhere. So it is undefined...it doesn't work. Like time travel or flying without equipment, it's never going to happen. Let it go and move on.

Answer 6

Division by zero is listed as 'undefined' It is actually impossible.

Division is separating something (say, a pizza) into a certain number of parts. You can't separate something into zero parts. Even with a disintegrating ray, you would make the item disappear, but it would have turned into billions of individual atoms, not able to be seen, but still not nothing.

Answer 7

Look at a weird example:

0/3 is 0. 0/5 is 0. 0/7 is 0. So,

0/3 = 0/5 = 0/7

so, 3 = 5 = 7 (!)

Make any sense? Nope. Even though it seems logical. That's why scientists took safe side and recomended not to spend your time thinking about this as no one can define this.

Answer 8

Boy, you see this question an awful lot. To be more acurate, only 0/0 is undefined, as it can be theoetically anything. This is a glib oversimplification, but you can think of calculus as finding out what 0/0 equals in various situations. As for 1/0, it is meaningless.

Answer 9

Try this; 8 divided by 2 means how many 2's does it take to make 8? Pretty easy, it takes 4 2's.

Now 8 divided by 0. How many 0's does it take to make 8. It just isn't going to happen. We can say an infinite number, call it undefined.

Answer 10

Imagine you had a cake. If you took a cake, and some one said cut it into 2 equally sized pieces, you would cut it in half. To cut it into one piece, you wouldn't cut it at all, you would have 1 piece already.

If somebody asked you to cut it into zero equally sized pieces there really wouldn't be anything you could do. Another way to look at it is that zero goes into any number and infinite amount of times, so it is undefined.