# Do we really know what is infinite in mathematics?

Surprising is our ability to do virtual appointments.We can give a name to business, processes and things that are virtual! Then we can talk and write about it. That goes so far as we start thinking that these things are really there!!

For example: Names of substances that we never found, even after centuries of searching, phlogiston, Aether and in Chemistry Substance Used in chemistry For Decades Turns Out To not Exist .

Another example: Language.We therefore appoint an ability that we cannot perceive directly.

Language We express, we use, we read, we hear, we speak. But pointing to language as object we can not.

Language escapes physical reality, it is not an object.However, we can point to the aforementioned physical reality of language expressions.

Infinity is also such a virtual object.We can talk about it, count it, image it. But we cannot pinpoint it.

Infinity is therefore easier to understand as a process, than as an Object!

How then?

The process of counting down: Take a large, super large number, e.g.A Googolplex Written Out … Count 1 on it, then there will always be a larger number.That process never ceases.

If we say that the collection of natural numbers 1, 2, 3,… is infinite, then that is 芒 鈧?虄echt芒 鈧劉.Give me a number and I can always add that number + 1 to the collection.

In addition, there are different forms of infinity.The natural and rational numbers are countable (you can enumerate them in theory), but the real numbers are not.

Infinity is an essential concept within mathematics, but it is also possible to define mathematics without infinity.One of my professors, Jean-Paul Van Bendegem, has dealt with this.

In projective geometry, Infinity is the intersection point of two parallel lines, and also 2 parallel planes meet, but on a line that is in infinity.

This point can then also be counted and that leads to totally new concepts and possibilities.

There are/come hopefully a bunch of good answers, I just want to point out a really great episode of the [insanely good BBC program Horizon:

To Infinity and Beyond

By Our third year, most of us will have learned to count.Once we know how, it seems as if there would be nothing to stop us counting forever. But, while Infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems.

Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last.And If the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you. Older than time, bigger than the universe and stranger than fiction. This is the story of Infinity.

Last on

Sat 10 Mar 2012 23:55

BBC FOUR

Good search on the internet I would say, and/or via a fake IP just do or you live in the UK [VPN IP simulators: Beware of malware/viruses