Infinity -- Some questions to clarify my understanding

[TheScienceOrca]

Homework Statement

I am trying to grasp infinity.

Homework Equations

Please tell me which are false and which are true (the statements).

If false explain why, don't just say because so and so said so, please EXPLAIN the concept otherwise I will never learn or explain the true answer!


Can infinity odd or even? If not what state is it in? Or the fact that it is never simply a static number, it is dynamic. Whatever the highest number you can think of at the time, infinity is FOR YOU.

Infinity is relative to the observer correct?


So infinity does have a limit?

Limit of f(x)=infinity as x approaches infinity = the highest number relative to the observer

That statement is essentially true correct?

If not why?

Also I read in the textbook x/infinity = 0.

But if you think about it nothing diving by anything will ever equal zero. Even if you think of THE largest number in the world it will get EXTREMELY close to zero but never get to it.

So why does it say EQUAL to 0?

That is just bad math in my books, why is that proper?
Thank you! I am calc first year now and school just started so I'm having some questions about limits.

The Attempt at a Solution

What?

 

[LCKurtz]

Homework Statement

I am trying to grasp infinity.

Homework Equations

Please tell me which are false and which are true (the statements).

If false explain why, don't just say because so and so said so, please EXPLAIN the concept otherwise I will never learn or explain the true answer!


Can infinity odd or even? If not what state is it in? Or the fact that it is never simply a static number, it is dynamic. Whatever the highest number you can think of at the time, infinity is FOR YOU.

Infinity is not a number. It is a symbol associated with something becoming unbounded.

Infinity is relative to the observer correct?

That question doesn't make sense to me.

So infinity does have a limit?

No. Infinity is a symbol representing a situation.

Limit of f(x)=infinity as x approaches infinity = the highest number relative to the observer

That statement is essentially true correct?

If not why?

What is this "relative to the observer"? That makes no sense. To say the limit of ##f(x)## as ##x\to a## is ##\infty## means as ##x## nears ##a##, ##f(x)## can be arbitrarily large. No number ##N## can bound it.

Also I read in the textbook x/infinity = 0.

But if you think about it nothing diving by anything will ever equal zero. Even if you think of THE largest number in the world it will get EXTREMELY close to zero but never get to it.

So why does it say EQUAL to 0?

You are correct that if ##x\ne 0##, no matter how large a number you divide it by, you won't get zero. So you could say the limit of ##x/N## is zero as ##N## "goes to infinity". It just gets closer and closer. That's the idea behind limits. It would never be correct to say ##x/N=0##. This will become clearer to you as you study limits.

 

[LCKurtz]

I now see this thread is a duplicate of https://www.physicsforums.com/showthread.php?t=771252.