Infinity/Infinity = ?; 0/0 = ?

[~Thor~]

What is infinity divided by infinity?

I think it is one, because if you look at the equation y=x/(x+1) as x approaches infinity, y approaches 1, then when x is infinity y=1. Since (infinity)=(infinity + 1), then (infinity/infinity)=1, if you look at the previous equation. However my IC (intro calc) teacher doesn't agree with me (although he never tells us what infinity/infinity is he just says it dangerous teritory).

What you think? And whats 0/0? Etc etc etc. (or infinity/0 or 0/infinitiy)

[Lord You]

What is infinity divided by infinity?

I think it is one, because if you look at the equation y=x/(x+1) as x approaches infinity, y approaches 1, then when x is infinity y=1. Since (infinity)=(infinity + 1), then (infinity/infinity)=1, if you look at the previous equation. However my IC (intro calc) teacher doesn't agree with me (although he never tells us what infinity/infinity is he just says it dangerous teritory).

What you think? And whats 0/0? Etc etc etc. (or infinity/0 or 0/infinitiy)

Isn't that a little bit like crossing the streams?

[Lord You]

Actually, it depends on what kind of infinity you are using. For example:

the limit as x->inf of 2x^2 + 3x - 4 is inf.
the limit as x->inf of 5x^2 - 2x + 100 is inf.

However, the limit as x-> inf of (2x^2 + 3x - 4)/(5x^2 - 2x + 100) is .4 For more information, look up l'Hôpital's rule.

[mazzmatazz]

Excel says 0/0=#DIV/0!

[Agent_Dark]

lol, dividing by 0 is not possible - it wont produce a result

[Lord You]

Excel says 0/0=#DIV/0!

Yes, but look at this:

Sin(0) = 0
0 = 0

but lim x->0 of (Sin(x))/x = 1

Excel ain't smart!

[mazzmatazz]

Yes, but look at this:

Sin(0) = 0
0 = 0

but lim x->0 of (Sin(x))/x = 1

Excel ain't smart!

I never said Excel was. I was going for the cheap laughs. I seem to have failed. *skulks off*

[Hudson]

Pointless fact: The US was testing F16`s near the black sea. on the first test run, they flew around for a bit, then all the onboard computers crashed. the daring pilot managed to land the plane. they found out that the black sea is below sea level (or something similar) and the altitude calculator was attempting to divide by a minus number, cause the insturments to crash.

</pointless fact>

[~Thor~]

I'm looking at stuff about l'Hôpital's rule now. Hopefully I can understand it. Maybe we'll deal with it next year in calc

[Lord You]

What's the limit of mazz's ego as my sarcasm approaches infinity?

Don't worry, I laughed.

[Agent_Dark]

Pointless fact: The US was testing F16`s near the black sea. on the first test run, they flew around for a bit, then all the onboard computers crashed. the daring pilot managed to land the plane. they found out that the black sea is below sea level (or something similar) and the altitude calculator was attempting to divide by a minus number, cause the insturments to crash.

</pointless fact>

lol
And also lol at your sig

[mazzmatazz]

What's the limit of mazz's ego as my sarcasm approaches infinity?

Don't worry, I laughed.

I'm not hurt by that comment

I'd like you to stop raiding my fridge though please. It's tiresome for me to keep buying more cheese and mayo

[lodellama]

While l'Hopital's rule involves ratios of infinities and zeros and will help with some tricky problems, it requires knowledge of the derivative, which you probably haven't covered yet. What you really want to do is spend more time looking at the broader topic of limits.

[Gregorius]

inf/inf = inf. iirc because both inf can be a different value.

0/0=inf because it give an infinate amount of answers (-inf =< x <= inf)

However, the limit as x-> inf of (2x^2 + 3x - 4)/(5x^2 - 2x + 100) is .4 For more information, look up l'Hôpital's rule.

Let me explain it

Lim 0-> inf : (2x^2+3x-4)/(5x^2-2x+100). First we take away the -4 and +100 since they're of no use, because with large number they're nothing. So we get:
Lim 0->inf : (2x^2+3x)/(5x^2-2x). Same goes for the 3x and -2x. So you get:
Lim 0->inf : (2x^2)/(5x^2). We can now apply basic algebra, which states Ca^P/Da^Q = (C/D)a^(P-Q). So if we apply that here we get:
Lim 0 ->inf: 0.4 * x^0 (x^0 = 1)

[Flyboy]

Anything divided by itself is 1. Infinity divided by itself is basically one huge number divided by itself. Hence it's one. No complex math needed.

Now what is a divide? It's splitting a number into a certain number of groups. If you split something into 0 groups then surely thats just 0.