Statistics

[Tex]

I don't know enough about stats or infinity to accurately answer this question:

1/∞

I assume it behaves like

.999999...=1

and therefore

1/∞=0

but wanted to check with someone who has studied math more than me.

Thanks!

[Joel]

If you were to draw it on a graph, it would get closer and closer to 0, but never touching.
Generally, in my classes at least, it is taken as 0.

[Tiberius]

1/∞ is as meaningless as 1/apple.

∞ is not a number. You cannot divide 1 by it.

Besides, if 1/∞=0, then you could multiple both sides by ∞ and get:

1(∞)/∞ = 0(∞)

...which gives...

∞/∞ = 0

...which means...

1 = 0

No.

If you were to draw it on a graph, it would get closer and closer to 0, but never touching.
Generally, in my classes at least, it is taken as 0.

Then either you have not understood your classes, or your professor is an idiot.

I believe you are thinking of the graph y = 1/x, where the y value tends towards zero as the value of x tends towards ∞. However, the value of y never becomes equal to 0, nor does the value of x become equal to ∞.

[Tex]

Ya, it doesn't work well with equations. Joel answered my question though, the asymptote would be X=0 as Y approaches infinity.

[Tiberius]

Ya, it doesn't work well with equations. Joel answered my question though, the asymptote would be X=0 as Y approaches infinity.

No it wouldn't.

"In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity."

Source: Wikipedia

X approaches 0. It never equals it. I just showed you what happens when X=0 when Y approaches infinity. Mathematics breaks down. 1 = 0 is a contradiction.

[Tex]

Ah, that makes more sense. Thank ya, sir.

[Faith No More]

"In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity."

Not to be a stickler here, but can't an asymptote be a curve that approaches any number but doesn't reach it? For example, there are asymptotes at 1 in f(x) = 1/(x-1).

[Tiberius]

No problem.

Incidentally, the reason why mathematics does not break down when dealing with infinitely long decimals (like 0.999999...) is down to the existence of real numbers, and being able to be placed on a number line between two others. That is to say, despite a number having an infinite number of digits after the decimal place, we can always find a number that is both higher and lower than it, without having to look at all the numbers (thus, we never actually need to expand the number to it's infinite length).

---

"In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity."

Not to be a stickler here, but can't an asymptote be a curve that approaches any number but doesn't reach it? For example, there are asymptotes at 1 in f(x) = 1/(x-1).

I think you've read the definition wrong.

It's not saying the asymptote itself is equal to 0, but that the distance between the curve and the line (the asymptote) approaches 0 (which holds true for any convergent number).

In your example, the distance between the curve of the function f(x) and the asymptote approaches 0.

[Kayenneh]

Tex, I absolutely suck at mathematics, but Vihart (is in my opinion both knowledgeable and explains many things math related well) and she made a nice video about the 0.9999...=1 conundrum.

---

http://www.youtube.com/watch?v=TINfzxSnnIE

---

[Joel]

1/∞ is as meaningless as 1/apple.

∞ is not a number. You cannot divide 1 by it.

Besides, if 1/∞=0, then you could multiple both sides by ∞ and get:

1(∞)/∞ = 0(∞)

...which gives...

∞/∞ = 0

...which means...

1 = 0

No.

If you were to draw it on a graph, it would get closer and closer to 0, but never touching.
Generally, in my classes at least, it is taken as 0.

Then either you have not understood your classes, or your professor is an idiot.

I believe you are thinking of the graph y = 1/x, where the y value tends towards zero as the value of x tends towards ∞. However, the value of y never becomes equal to 0, nor does the value of x become equal to ∞.

He tells us that when it so close to zero, we should just write it as zero.