Theoretical!

[blaster009]

Yar har har. Let's argue why or why not anything divided by ∞ is 0, and if it should work the other way.

To ponder (where n is any real number):

n/∞ = 0
n/0 = ∞
0/0 = Undefined (instead of 1)
∞/∞ = Undefined (instead of 1)

[md]

n/x as x-> ∞ = 0. Likewise n/x as x -> 0 = ∞. That's not the same as n/∞=0 or n/0 = ∞.

Infinites are difficult in math... they tend to break people's minds

[rizzix]

pshhht..

n/x -> 0 as x -> ∞
and
n/x -> ∞ as x -> 0

[codemage]

Cornflake wrote:

Infinites are difficult in math... they tend to break people's minds

That's because infinity doesn't really have a place in reality. It's a mathematical abstraction. Most people can't get over Zeno's paradox.

[Andy]

the way my highschool physics teacher described it, infinity is just a sign post somewhere, once you past that sign post, you're in infinity land haha..

i miss physics

[Cervantes]

blaster009 wrote:

0/0 = Undefined (instead of 1)

I have my own little theory about this one. It represents any number. This sort of comes through when solving limits that go to 0/0.

Better yet, set 0/0 to x and solve for x.

x = 0/0
0x = 0

Any value of x satisfies this equation, and so 0/0 represents any number.

Similarly for ∞/∞

[Andy]

you cant multiply both sides of an equation by 0 and use it as a valid argument

[MysticVegeta]

yup andy is right.

say: x = 0/5
5x = 0
x must be 0, other #s dont satisfy

[md]

MysticVegeta wrote:

yup andy is right.

say: x = 0/5
5x = 0
x must be 0, other #s dont satisfy

Umm... that's a totally different arguement...

And rizzix; that's what I said. Aproaches is not the same as equals... another thing people don't always understand.

0/0 is undefined (not 1) as you cannot divide anything by nothing (not even nothing). ∞/∞ is one because the two ∞'s cancel out (just as any two variables of the same name and power would.

[Cervantes]

MysticVegeta wrote:

yup andy is right.

say: x = 0/5
5x = 0
x must be 0, other #s dont satisfy

Aw great, now I've got water all over my monitor. Well, not really, but I thought I'd say that anyways because it neatly described my reaction. If I happened to have had water in my mouth at the time, that would have been the outcome.
MysticVegeta, 0/5 is 0.

Andy wrote:

you cant multiply both sides of an equation by 0 and use it as a valid argument

Why not? It's a tricky reason to articulate, I'm sure.

Now that I've thought about it a bit more, I'm thinking you're right. My reason: multiplying both sides by zero (which is a perfectly legal operation) gives:
0x = (0 / 0) * 0
Not what I previously had:
0x = 0
which assumed that 0/0 was 1.

[Andy]

the simplest way to look at 0/a a/0 and 0/0 is

if you have 0 apples and try to split it with a people, each person gets 0
thus 0/a = 0

if you have a apples and try to split it with 0 people,we have nobody to ask about how many apples they recieved all we know is the a apples disappeared.
thus a/0 is undefined

and if you have 0 apples split betwen 0 people, then we cannot determine how many apples each person recieved since we had no proof of the apple, and no body to tell us what happened
thus 0/0 is indeterminate

[Mazer]

I took the apples, Andy. I took the apples, and I threw them at your windows. Then when your neighbours saw me I blamed it on the ten year old kid who happened to be riding by at the time. The police want to know if you'll be pressing charges.

[jamonathin]

lmao mazer . . but yeah, any way your slice it, it's still going to turn out the way Andy explained it. No matter what variables you stick in there.

But here's something . .

Let's say n / x = 0 then

n = 0x

1 = 0x / n

1 = 0 / n

1 = 0 ?

Did I miss something or does there have to be restrictions for n (n = 0, n E R). .

[md]

No restriction because take n = 0

n = 0x
0 = 0x
0 = 0

[Martin]

Or we can get into exciting things to confuse people such as that 0.99.. = 1.

The big problem that people have with infinities is that they think of it as a really big number, which it isn't. Infinity is a concept, not a number. There is no number that equals 'infinity,' because infinity is NOT a number. Once you get over that, it's much easier.

As such, something like 1/infinity has no meaning, because you're dividing a number (1) by not a number (infinity). This makes a number of operations useless on infinity, such as addition (infinity + 1 anyone?). It's like asking what 5 + purple is - it doesn't make any sense.

When you're saying 1/infinity, for the most part you're saying 1/BIG, which tends to zero as BIG gets bigger. What this means is that you can get arbitrarily close to zero - give me a positive distance to zero, and I can make it so that 1/BIG is within that distance.