Infinity Paradox

By LUKE MCGOVERN
Published: May 20, 2008

Infinity is an abstract concept of unboundedness which can perhaps be paralleled by the realm of our own Universe. In mathematics, infinity can take different forms depending on the situation in which it is used. It generally marks a limit of a value but it is not a limit in itself. It is paradoxical concept that allows the paradox - of there being no such thing as a final number - to not get in the way of some great concepts.

When looking at numbers, infinity pokes its head up quite often. There is positive infinity, negative infinity, infinity between 0 and 1 in a fractional sense - e.g. 0.0001..., and there is also infinity in a constant such Pi. Division by zero also seems to mess with the infinite. For the sake of sanity, the paradox that is infinity is abstracted out which allows mathematics get down to the nitty-gritty.

Can there be so many infinities as mentioned above or are they all belonging to same infinite but just viewed differently? The latter perhaps seems more likely. While not trying to jump to a conclusion too quickly, perhaps the infinite we are trying to model is that of the infinite we face in our environment - the Universe itself.

If Pi is a constant and an infinity at the same time, is not the value "1" much the same as Pi - e.g. 1.00000...?

It could be said that infinity still belongs to each value in mathematics but does it make any sense to focus on this fact or realise it in anyway? Perhaps not in most fields, but artificial intelligence might just be concerned with such issues.