I confess I’m a fan of mathematics. There is an inherent beauty in a well put together mathematical formulae. Maths has absolute precision and reveals the hidden world of logic and form, but only if our reasoning and equations are sound (get a grip, Flaxen). Yet most folk are oblivious and see mathematics as simply a tool to count their money or enumerate their woes; pity. That said, mathematics has its mavericks, ideas and concepts which defy formal logical and mathematic analysis- they cannot be proved or refuted; infinity is such a concept.
What is infinity? Let's start with a formal definition and follow up with a deceptively simple exposition. First off, infinity is not a number, it is an abstract notion and usually, but not exclusively, represented by the symbol, ∞ (lemniscate). The following sequence represents an infinite number sequence in both directions:
Clearly the numbers can be extended forever. Even if you think of a very large number you can always think of a larger number just by adding 1. Similarly, there exists an infinite series of numbers between the integers, 1 and 2. Pi is another example and represents the ratio of the circumference of any circle divided by its diameter. Pi (π) can be written as 22/7, or more usually: 3.14159265359. In this instance, Pi is calculated to 11 decimal places. Recently, mathematicians, with the help of a computer, have calculated Pi to 10 trillion digits! Pi goes on forever without ever lapsing into a discernable repeating pattern of numbers. Clearly some folk have way too much time on their hands. Although to be fair, mathematicians tend toward the obsessive (barking mad).
There are no numbers larger than infinity although the infinite set of whole numbers is twice as large as the infinite set of even whole numbers- confused? If not, you haven't understood the concept.
Moving swiftly on to cosmology. Many theoretical physicists are of the opinion that the universe is infinitely large. This is so counterintuitive that it defies contemplation by the human mind. While we may be comfortable with a series of infinite numbers, the realm of the real physical world, as it is experienced at least, is circumscribed by finite limits. How can infinity apply to our universe of material existence? The contrary possibility that the universe is finite and has bounds is equally disturbing. Although we can conceive of a closed but extremely large universe, we run into problems when we ask the question: what lies outside the encapsulated universe? The glib answer is: nothing. Nothing can exist outside the universe, or can it? To be honest, I don’t have satisfactory answers to questions, paradoxes and conundrums which have troubled brilliant minds for over two and half millennia. Perhaps there are certain areas of thought where questions should not be asked (an anathema to the scientist). For to do so is to embrace folly and thereby become mired and entangled in a web of inconsistencies and contradictions. "Whereof one cannot speak, thereof one must be silent".
If things ain't weird enough, contemplate this. If the universe is truly infinite then it logically follows that there must be an infinite number of 'earths' and on some of these alternate worlds an identical copy of you exists mirroring your entire life. It also means that an alternative ‘you’ exists where the only difference is one of eye colour. Every conceivable possibility and every inconceivable possibility exists. The only limits would be the limits imposed by the natural laws of our universe. But what if there exists an infinite number of universes each with its own peculiar set of physical laws and constants? I'll leave you to ponder on these dark possibilities for as long as your sanity will allow........
In these circumstances, the finite enclosed universe seems like a sane alternative.