If a mathematician wants to explore infinity, there are many options - for example by calculating π , or the square root of 2, or dividing any number by 0.

For philosophers, the concept of infinity is fraught with enigmas :

• Are infinities created over time different from instant infinities?
• Is it necessary to have an infinite universe to accommodate infinities (going against the prevalent current opinion about the universe)?
• Is it possible to sub-divide something an infinite number of times (going against quantum theory)?
• If it's possible to 'prove' something by the use of logic, but the proof is infinitely long, is it proven?

Such questions (and others) are on record as having been considered for at least 2,000 years - without, as yet, any general agreement.

Further reading with examples The Internet Encyclopedia of Philosophy (IEP), University of Tennessee.

Also see : 'Beyond Infinty' Australian Academy of Science.