2nd Free Coin(s) Give Away!

edit:
Well shoewrecky got the answer I was looking for... CONGRATS!
CONTEST OVER

Okay. Here is the second of my weekly coin give-away contest!
This week I have 2 wheat pennies, a steel wheat penny (1943), a silver dime, and a blue toned nickel up for grabs! (photos below)

The contest this week is simple.
I am in love with math so here is my question.

answer the two following questions in full:

0/0 = ?
5/0 = ?

The answer I'm looking for is NOT, "you can not divide by zero", I want creative answers. (USE THE HINT PROVIDED BELOW)
hint: asymptote

everyone gets one shot at answering this.
Have fun!

(disclaimer: the photo of the blue nickel really brings out the blue-ness.. in real life it is still very blue just not as noticeable as the photo makes it out to be, sorry for my camera. But it is still a very beautiful shade of blue)

 

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As the line approaches zero its curves into infinity. Horizontal, vertical, and oblique are the three main types. Y=F(X) can be used to solve it. You can use a lim or plus or minor f(x) to infinity to get your answer for both horizonal and vertical, so my simple answer would be the line curves into infinity as it heads towards the intersect of 0. My answer is infinity, and there are 3 different ways of solving it.

 

Very good, however it is not the answer I'm looking for...
It isn't even the FULL answer.

 

asymptote can have 3 different ways of solving with 3 different line angles and degrees providing 12 different answers, which are you lookinh for?

 

Well if I answered that then the contest would be over now wouldn't it.

 

Can you specify? Are you looking for what the limit is as they approach infinity?

 

0/0 = indeterminate as you could conceivably give it any number of values

5/0 = is undefined because division is defined in terms of multiplication. a/b = x is defined to mean that b*x = a. There is no x such that 0*x = 5, since 0*x = 0 for all x. Thus 5/0 does not exist, or is not defined, or is undefined.

 

Isnt that the samething as 0 or infinity.

 

0/0 = ? 1. Any number divided by itself equals one.
5/0 = ? infinity. As the divisor becomes smaller, the answer becomes larger. As the divisor becomes infinitely small, the answer becomes infinitely large - i,e, infinity.

 

The answer for 0/0 is indeterminate form.It is impossible to determine, without context what it represents. And for 5/0 is undefined.there is no answer because This would mean that the answer x 0 = 5. But anything that is times 0 always equals 0.

 

great minds think alike!

 

yeah! You must be a lot faster at typing then me! haha! When I started typing it the only one that answed was Hunt1!

 

to specify... I want to concept it approaches.
still no one has the answer I'm looking for.

and for everyone who said it's undefined because you can't divide by zero..
look at my original post "The answer I'm looking for is NOT, 'you can not divide by zero'"

hehe
also the 0/0 = 1.. any number divided by itself equals one thing made me chuckle
That's only partially correct hehe.

 

ok my definition
0 / 0 = 0+0 = 0 x 0 = 0 - 0 = ?
5/0 = 5.0 or piggies / smokies / bears / popo's /cops

Real Answer from Mathforum.org (I take no credit unless it's right )

L'Hopital's rule does *not* tell you what 0/0 is, because 0/0 is what is called an "indeterminate" quantity, which is to say that its value depends on what the situation is. To convince your friends of this, ask them the following question: "Find the limit of (ax)/x as a approaches 0 by using L'Hopital's
rule." But if you just put x = 0 in this expression, you get 0/0. So, according to L'Hopital, 0/0 is equal to a.

Did you notice that I didn't say what "a" was? That's because it doesn't matter. You can pick a equal to anything you want. For instance, you could pick a = 1. Then you would get 0/0 = 1

Or pick a = - 3.14159. Then: 0/0 = - 3.14159.

So as you can see, 0/0 can be anything you want it to be. On the other hand, in a particular problem, 0/0 might turn out to be something very precise (and that's where you really do need calculus to understand it!). I think your argument for why 0/0 is undefined is a really good one.

However, I have another way of understanding why 0/0 doesn't make sense, and it goes like this. One way of understanding the fraction a/b is to think of it as the answer to the following question:

"If I had a dollars, and b friends, and I distributed those a dollars equally amongst my b friends, then how much money would each of my friends get?"

The answer is that they would each get a/b dollars. You can see that this works for fractions like 6/3, or 5/10, and so on.

But try it for 0/3. If you have 0 dollars, and 3 friends, and you distribute those 0 dollars (you're feeling generous...) equally amongst each of them, how much would each of your 3 friends get? Clearly, they would each get 0 dollars!

Now try it for 3/0. If you have 3 dollars and 0 friends, and you....but how can you distribute any amount of money amongst friends who don't exist? So the question of what 3/0 means makes no sense!

Now here's the kicker: What if you have 0 dollars and 0 friends? If you distribute those 0 dollars equally amongst your 0 friends, how much does each of those (nonexistent) friends get? Do you see that this question makes no sense either? In particular, if 0/0 = 1, then that would mean that each of your nonexistent friends got 1 dollar!
How could that be? Where would that dollar have come from?

5/0 = ?
The reason is related to the associated multiplication question. If you divide 6 by 3 the answer is 2 because 2 times 3 IS 6. If you divide 6 by zero, then you are asking the question, "What number times zero gives 6?" The answer to that one, of course, is no number, for we know that zero times any real number is zero not 6. So we say that
division by zero is undefined, for it is not consistent with division by other numbers.

For example, we could say that 1/0 = 5. But there's a rule in arithmetic that a(b/a) = b, and if 1/0 = 5, 0(1/0) = 0*5 = 0 doesn't work, so you could never use the rule. If you changed every rule to specifically say that it doesn't work for zero in the denominator, what's the point of making 1/0 = 5 in the first place? You can't use any rules on it.

But maybe you're thinking of saying that 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other
equations?

Does infinity - infinity = 0?
Does 1 + infinity = infinity?

If so, the associative rule doesn't work, since (a+b)+c = a+(b+c) will not always work:

1 + (infinity - infinity) = 1 + 0 = 1, but (1 + infinity) - infinity = infinity - infinity = 0.

You can try to make up a good set of rules, but it always leads to nonsense, so to avoid all the trouble we just say that it doesn't make sense to divide by zero.

What happens if you add apples to oranges? It just doesn't make sense, so the easiest thing is just to say that it doesn't make sense, or, as a mathematician would say, "it is undefined".

Maybe that's the best way to look at it. When, in mathematics, you see a statement like "operation XYZ is undefined", you should translate it in your head to "operation XYZ doesn't make sense".

 

My mom had a baby once.

 

Then great minds need to learn how to read the question. "The answer I'm looking for is NOT, 'you can not divide by zero'". All you have done is say what he says he does not want as an answer in another way.

 

and all he did was cut and paste a Wikipedia definition but I wanted to know why his explanation for his first edit included the term "forumula". Is that a formula you use in a forum?

 

I am still standing by infinity alone, if we only get 1 answer with 12 different answers, we could only get it right after three months assuming he allows 1 answer per week...

 

Anyone can post anything from anywhere, he didnt say we could use resources

 

I'm starting Calc 3 next month, but you question does not make much sense. It's not even a function, so there cannot be an asyptope. I think i might see what your going at though.

1. zero
2. infinity