reciprocal ratio of infinity ?

[Physicsfan]

anything by zero is infinity.but is anything by infinity zero?

[the tree]

anything by zero is infinity.

No.

but is anything by infinity zero?

No.

 

Division by zero is undefined, likewise for infinity.

[Physicsfan]

but devision by zero is taken as infinity in trignometry.

tan 90 for example.

[the tree]

The tangent function isn't defined at 90 degrees either - particularly in trigonometry there does not exist a Euclidean triangle with two right angles so the trigonometric definition tells you that the function isn't defined at that point.

[ajb]

You should think of zero as the only non-invertible element in the real line. That is you do not have an element say [math]0^{-1}[/math] such that [math]0^{-1}0 = 0 0^{-1} = 1[/math]. In other words, as the tree has said you cannot divide by zero.

 

Now, [math]\pm \infty[/math] are not real numbers, so there is no reason why they should obey the rules of real numbers. Specifically, division and multiplication by infinity need not be defined.

 

Sometimes it is useful to extend the real numbers by formal elements as [math]\mathbb{R}\cup \{\infty\} \cup \{-\infty\}[/math], but that is probably another story.

[Physicsfan]

Isn't division by zero similar to asking "how many points there are in a line"?

that would be infinite wouldn't it?

[the tree]

Isn't division by zero similar to asking "how many points there are in a line"?

Division is the inverse operation to multiplication. Division of [imath]x[/imath] by zero is asking: "what number multiplied by zero gives [imath]x[/imath]?".

that would be infinite wouldn't it?

It'd be [imath]\aleph_1[/imath] which, whilst infinite, is an entirely different beast to [imath]^{+} \infty[/imath]. Edited May 13, 2010 by the tree
-typo

[Physicsfan]

x[/imath']?".

 

the "number" would be the quotient.

So, my statement and yours would mean the same.

Because both equal infinity.

 

this kind of concept is also seen in reflection between two parallel mirrors.

(360/0)-1=infinity.(0 is the angle between the two mirrors.)

thats the reason we get countless images when we stand between two parallel mirrors.

Edited May 13, 2010 by Physicsfan

[the tree]

the "number" would be the quotient.

So, my statement and yours would mean the same.

Because both equal infinity.

 

Right, okay, whatever. So you're saying that [imath]5 \div 0=\infty[/imath] and that subsequently [imath]\infty \cdot 0 = 5[/imath]? Presumably you're also saying [imath]7 \div 0=\infty[/imath] and that subsequently [imath]\infty \cdot 0 = 7[/imath]? What else is [imath]\infty \cdot 0[/imath] equal to?

 

Seriously though, there is no inverse operation to multiplication by zero. In other words, division by zero is just undefined. You're not going to find a way around that.

 

this kind of concept is also seen in reflection between two parallel mirrors.

(360/0)-1=infinity.(0 is the angle between the two mirrors.)

thats the reason we get countless images when we stand between two parallel mirrors.

No it isn't. Mirrors follow normal rules of geometry that can be described using well defined mathematics.

[ewmon]

Yes, zero is not as innocent as it seems. It means “nothing” – literally -- “no thing”, and so in units, no x, no y, no z, or no atoms, no grams, no wombats, no meters, no galaxies, … So when taking the reciprocal, what are the units of the quotient? The possibilities are infinite. This is another way of looking at infinity as “undefined”. It's only when we step slightly away from zero or infinity do we find ourselves on a dimension in reality.

[Physicsfan]

So you're saying that [imath]5 \div 0=\infty[/imath] and that subsequently [imath]\infty \cdot 0 = 5[/imath]? Presumably you're also saying [imath]7 \div 0=\infty[/imath] and that subsequently [imath]\infty \cdot 0 = 7[/imath]?

 

no.

i was talking about 1/infinity.thats what i was actually asking about.(refer to my first post)

this question hit me because if tan 90 is infinite(theoretically) then cot 90 is 1/infinite right? so how should i explain this?

[the tree]

i was talking about 1/infinity

That is again, just as undefined as it as ever it was.

this question hit me because if tan 90 is infinite(theoretically)

It is not.

then cot 90 is 1/infinite right?

[math]\cot 90 = \frac{\cos 90 }{\sin {90}}[/math]

or

[math]\cot 90 = \lim_{\theta \to 90} \frac{1}{\tan \theta}[/math] with the condition of continuity.

[Cap'n Refsmmat]

More importantly, [math]\lim_{\theta \to 90} \tan \theta[/math] does not exist, because [math]\tan \theta[/math] approaches [math]\infty[/math] from the left and [math]-\infty[/math] from the right.

 

So [math]\tan 90[/math] cannot be said to be [math]\infty[/math].