Infinity is a useful concept but it is often used inappropriately by being assigned as a trait to some object or another. Briefly, nothing can be infinite, since in order for something to "be", it must be defined and measurable. If it isn't, then the object would exist in a perpetual state of creation and couldn't be said to "be" anything at all ... yet.
This problem is aggravated by the assumption that since the concept of infinity has utility in mathematics, that it somehow represents something that is translatable and definable. As an example, in mathematics we understand that pi is an infinite irrational number. However, in practical terms, this is a meaningless concept. To claim a number is infinite is to render it incomplete, or "under construction". It makes it unknowable since its value can never be established. It is only by making the infinite "finite", that we acquire its utility value. In short, pi is meaningful only when it isn't infinite. An infinite number is incomplete and unknown, and only acquires meaning when an "end" is established.
Therefore pi is an infinite irrational number, in principle only. What this suggests is that the process of declaring something infinite, is not in the object itself, but rather in the steps that one can take to determine a particular value or end point. Essentially infinity is an act of measurement or counting only and describes the condition where there is no procedural restriction on the number of iterations (counting or measuring) that one can engage in.
Infinity is an imaginary concept that the mind has created (1). We can't actually imagine it, since that would result in a mentally recursive process. Even when we say that a set of numbers is infinite, we are only considering this "in principle". Numbers don't exist except in our minds. So, if we argue that an infinite set of numbers exists, then what do we mean if we can never actually count them? We can recognize the absurdity of the situation by considering that an infinite number means that we could have a number larger than all the particles in the universe. What would it mean to have a number larger than all the objects that one could actually count? or a number larger than the time available to count it?
In this context, infinity doesn't specifically define the set of number, but rather defines the process by which we can create the next number in any proposed sequence. It doesn't describe the numbers; it describes the means by which they can be created.
This causes a different perspective be applied to situations in which infinity is routinely invoked to make an argument (generally to improve the probability). As an example, consider how infinity is often used to argue for the inevitability of life being discovered (or existing) on other planets. After all, in an infinite universe with infinite contents, then the result must always assure that there be an infinite supply of habitable planets and civilizations. However, if we invoke infinity, then we invoke the requirement that our claimed object (i.e. the universe) is unmeasurable, which further argues that the existence of life on other planets is correspondingly unknowable. Basically, we're left right where we were all along. In the absence of actually discovering life on another planet, we can gain no reassurance by the invocation of infinities to make the numbers work better.
Infinity is an extremely useful concept when it is employed to describe a process were iterative steps, counting, or measurement are involved, but to consider it an actual trait, simply reduces the object to which it is being applied to an imaginary product of the human brain.
(1) This is similar to the definition of a line and point in geometry, which are dimensionless, and how it differs from "real" world expressions.
What About Infinity?