These are numbers that go on forever. And ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever, and ever... Get the point? Infinity is an infinite number and it exists so therefore don't infinite numbers exist?
Define the set of natural numbers as beginning with 1, and for any number n, the number after it is n+1. Theorem: The set is infinite. Proof: Suppose not. Then there exists a greatest number, call it N. Because N is a number in the set, then N+1 is also in the set. But N is the greatest number, so N > N+1, therefore 0 > 1, which is a contradiction.
So we humans can create a set that logically has an infinite number of things in it. Does the Universe have an infinite or finite set of particles? That is an open question in physics. Can we divide things into infinitely smaller pieces? No because we run into Planck distances. Does that answer the question? No because it's an ill-posed question.
"Perception" is something limited in an awareness that can only evolve from a part to the whole or from the whole to a part principle of initiation. (Parts and whole are equated to "finite" and "infinite" in "Mereology: The Origins of Garlic Cures and the Art of Telling a Tale of Ragout"). In the Garlic Cures, arithmetic and geometry are referred to as "building blocks in deliverance" or "moving parts" of the existence to life relationship. In the first impressions of such a judgment (in a post Cartesian awareness) there appears to be a revealed a point of objective contention to or in their natures: Numbers and geometrical forms seem to appear independently of "one's" experience -- or they necessarily exist independent of "one's" consciousness. How does the Garlic Cures address this issue? Garlic delivers numbers and geometrical forms in a non-Cartesian story.... There is only a "difference" in the beginning and end of the discussion. In other words, infinite and finite are the one and the same. They are simply the two sides of the same coin "in toss". http://birddogbooks.com/bdb/
Albert Einstein — 'Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.'
How so ever vast our universe may be it is definitely not infinite. If we consider infinity it gives rise to so many paradoxes and these are unresolved. These paradoxes associated with infinity proves that there can not be a true infinity. For example, if we take out something from infinity it still remains as infinity. It is so counterintuitive and hence can not be true.
Is there really such a thing as "infinity"?
It's a tough question, because the word "infinity" can mean different things in different contexts.
In mathematics, whether or not a certain concept exists can depend on the context in which you ask the question. If you want to know more about this, you can refer to a fuller explanation of how a mathematical concept can exist in some contexts but not in others.
Here are some of the contexts in which the question "is there such a thing as infinity" can be asked, and the answers appropriate for each context. The details are given afterwards.
1.In the context of a number system,
in which "infinity" would mean something one can treat like a number.
In this context, infinity does not exist.
2.In the context of a topological space,
in which "infinity" would mean something that certain sequences of numbers converge to.
In this context, infinity does exist.
3.In the context of measuring sizes of sets,
in which "infinity" means a measurement of the size of an infinite set.
In this context, such "infinity" concepts do exist but there are more than one of them, since not all infinite sets have the same size. So there does not exist any one single "infinity" concept; instead, there exists a whole collection of things called "infinite cardinal numbers".