Does an equation containing infinity not equal 0 or infinity exist? Does an equation containing infinity which is not equal to 0 or infinity exist? My math education stopped at poorly understanding trig so don't kill me please.
OK so the question I meant to ask was if any 'operation'? using infinity as a 'factor'? will yield 0 or +- infinity. I was looking at it as if infinity is a black hole which gobbles up everything on its side of the equals, then the equals it self as well, then the other side provided its never x0. The only thing capable of rendering not infinity is to multiply (or divide right?) by 0 or minus infinity. From what I understand now the symbol for infinity represents the possibility of an ever increasing number that is not finite...not necessarily "infinity" or infinite. So... can it be said that no function\equation\operation\expression even contains an infinite number as it would brick said action?

The function that you are thinking about is a function with asymptotes. For example, $f(x)=\dfrac{1}{x}$ never reaches $x=0$. Similarly, other functions only exist within certain domains and ranges,depending  on the function itself. So, to answer your question, yes, functions which neither pass through 0 or approach $\infty$ do exist. In fact, they are often in common use in math.
