A few questions.

[Howard]

Does 1 divided by infinity equal 0?

Also, is a regular polygon with an infinite number of sides a circle?

 

[Indolent]

Yeah, any number divided by infinity equals zero. Don't know about the circle one though...

 

[Lynx516]

Technically no!

this is due to what infinity is
infinity is NOT a number it is a concept. You cannot do arithmatic with it except have things tend to infinity.

 

[Lynx516]

double post

 

[Mingon]

this is due to what infinity is infinity is NOT a number it is a concept. You cannot do arithmatic with it except have things tend to infinity.

Doesnt this depends on the type of infinity you are thinking about

Also, is a regular polygon with an infinite number of sides a circle?

No it might resemble a circle but it isnt.

 

[mindfire]

ok.. i just had physics class today and the same question was asked!
1 divided by infinity equals zero
dont argue..

 

[Ultimaix]

If you replace infinity by lim(x->infinity) x, then yes to both.
So lim(x->infiny) 1/x = 0, and an x-sided regular polygon as x approaches infinity is a circle.

 

[Mingon]

ok.. i just had physics class today and the same question was asked!1 divided by infinity equals zero
dont argue..

Dont take this personal - but have you stopped to think it over yourself? Not all physics teachers know everything (I had this argument with my maths lecturer on something similar). Their are at least 5 types of infinity. The two that spring to mind (alpha null?) are what confuses people the most. The first is continuous numbers e.g. 1+1, etc..The second is the type of infinity that as soon as you start to to imagine how big it is - your wrong its infinitesimally bigger (big word - bad spelling, probably).
The question was does 1 divided by infinity = 0 the answer is no - unless you disregard the infinite number of decimals places and set a significant digits no. so the answer will be be more zero than 1 but it still wont be exactly 1. The same applies to the circle an infinite amount of polygons might look like a curved surface but it isnt its just almost their.

So basically 0.0000000000000000000000000000000000000000000000000000000000000000000000000000001 is not zero but its close, and if your only looking for an answer to within the odd million digits then it will appear to be zero - but only because you have set a limit (which you cant when thinking of infinity).

The main problem with both of these is that you cant calculate infinity its just not possible and so when doing any sort of calculation based on infinity you have to assume its 0 and as the error is so minute it 'shouldnt' make to much of an error.


Side note - if this comes over badly sorry I have asberger's and my 'speciality' is practical physics.

 

[gururu]

By principle alone, a circle has no sides.

1 divided by infinity does not equal zero, it approaches zero.
But you cannot say it ever equals zero, because it NEVER reaches zero.
For mathematics we sometimes substitute for zero, but this is only to simplify the term.
It is generally ok, since the term can contribute nothing relative to other terms in the equation.

 

[wviperw]

The limit of 1/n as n->infinite is 0, but 1/n where n=infinite doesn't work because, as stated, infinite isn't a workable number but a concept.

A regular polygon with infinite sides is exactly that--a regular polygon with infinite sides.

There's a crucial distinction between concept and practice. Where a lot of people get tripped up is when they try to apply practice to concept when that isn't supposed to happen.