That depends on what you mean by "reality". To experience infinity appears to be impossible, I would say, and the same goes for the "infinitesimally small". It is a construct by our brains - our theoretical models -, and not of our senses. 

That depends on what you mean by "reality". To experience infinity appears to be impossible, I would say, and the same goes for the "infinitesimally small". It is a construct by our brains - our theoretical models -, and not of our senses. 

I'm sorry Michael, I wasn't clear enought! So, I mean in practice.

Most schools of philosophy in BCE distinguished between the ponderable and the imponderable, the finite and the infinite. Reality once applied only to the infinite and the physical was called maya (illusion). Now the reverse is the case. Projective geometry can help to make the experience practical. See http://nct.goetheanum.org.

This is a good question with not so obvious answers.

One source of answers to this question is from perspective in art and mathematics.   Each of us has more than likely perceived lines converging to a point (at infinity) in the distant horizon.   For example, the is a common perception for those who have been waiting for train, looking down empty train tracks seemingly converging to a point along a distant horizon.    It is this perception of infinity that routinely used by artists to suggest depth in a painting or drawing on a 2D surface.   

The perception of seemingly infinitely small objects can be seen with an ordinary microscope.    Consider, for example, the progression of cubes from fairly large to very small in an etched diamond surface (see the attached image).   The physicist S. Tolanksy used a chemical process to attack a diamond surface to produce microscopic blocks in the attached image.    In any case, the perception of infinitely small or the infinitely large is every day experience.   Beyond perception, it becomes necessary to use mathematics to reason about infinities.

Some would argue that mathematics is reality.    In that case, the puzzle about perceived infinities vanishes.

Dear Marcelo Negri Soares, as far as I know, the infinity, in practice, may  exsit, but sometimes cannot be measured or detected. For a simple example, when we construct the subgrad, the soil particles may be considered infinity, as they are cannot be accurately messured. May this can help you.

For me, practically, infinity does not exist.I am aware that all specific things on earth and in the universe must pass.

But philosophically, it does.

If there is such a thing as constant change, I believe there could also be a finite infinity.

Or a changing constant and an infinite finite.

Dear Marcelo,

The term infinity is used  to indicate the sense "endless". It has some sense in real life. There are so many things we can not count or measure. Fro example, the quantity of water in the sea on earth.  I don't know whether we can measure  it accurately.

In Mathematics,  there are two types of infinity, countable and uncountable. Countable means we know the predecessor and successor of any element of the system. Uncountable infinity stands for the system where the predecessor and successor of any element is  not known to us.  The concept is relevant in Mathematics and has lot significance in Mathematical calculations. Since Mathematics is the language of nature,  the concept of infinity has significance in nature too..

It may be possible to count the number of wild animals in a forest. Will it be possible to count the number of insects in the same area? Can we practically count the number of sand particles in a beach?  But we know that there is a quantity for all these. That quantity is infinity, as per my knowledge.

Infinity is a very good notion for practically approximate huge quantities. I give here some examples:

- Archimedes' number of sand grains. The easiest approximation is of course "infinity".

- Look at a railway in perspective. Everyone has the illusion that the two parallel lines meet somewhere at the horizont. By the abstractisation of projective geometry, they meet at infinity.

- Which is the biggest natural number? Of course, if you say n, I say n+1. So it is practical to consider N infinite.

- Let P(A) be the set of subsets of A. I repeat here the argument that P(A) is always a bigger set than A. Suppose that it wouldn't be so, and that f: A ---> P(A) would be surjective. Consider the set B = { x in A | x does not belong to f(x) }. B is a subset of A, f is surjective, so there is a b in A such that f(b) = B. Now b is in B if and only if b is in f(b) if and only if b is not in B. Contradiction.

The only practical way to solve this dilemma, is to suppose that the sequence N, P(N), P(P(N)),... contains an infinity of infinite sets, where every one is strictly bigger than its predecessor. This way we accept that there are different infinities, and that some of them are bigger than others. Continuum is bigger than the countable infinity, etc.

So infinity seems to be a practical solution to approximate huge sets and to excape logical paradoxes. 

Yes it exists and very simple. new philosophical view merging infinity, imaginary number and zero

Article New Philosophical View Merging Infinity, Imaginary number an...