What is difference between infinite and undefined in terms of mathematics ?

Question

I search most of the article available in the internet, but i am able to clear on this two statement

1/0 is undefined or infinity.
1/infinite is zero or undefined.

But i am clear about the things if we will use lim (x->infinite) 1/x approaches to zero

Answer 1

Let me put my perspective (may not be the answer) though we don't support maths as vertical but never mind -

say you have a number like .33333333....... where 3 is repeated infinitely but is a defined number, say you have a number which is equivalent to the number of atoms in the universe which is infinite but a defined number.

When we come to 1/0 its undefined number as it is not a capability issue but number does not exist.

Love to receive the perspective of others :)

Answer 2

Let us consider THE EQUATION
X^2-4=x^2-4
In this ... any given value satisfies the equation
This equation is said to have infinitely many solutions
But if I take the equation
0x=2
Here no value satisfies the equation and therefore has
NO SOLUTION AT ALL
THIS IS SAID TO UNDEFINED AS WE CANNOT ARRIVE. AT A CONCLUSION THAT WHAT IS THE VALUE OF X
Furthermore if some says that x= 2/0
Now the question arises what is 2/0
We cannot divide anything by zero.... so it is said it is undefined