A road named NoNameUno

Today, the 14th of March is Pi ( 3.14...) day!. Does it mean it's an irrational day!! Perhaps not...

There is an interesting constructive approach to show that there are irrational numbers. IIRC, Cantor had the constructive method to show that the number system ( i.e. the real number systems) does have other numbers beside rational numbers ( intergers happen to be the degenrate case of rational number, since the denominator is trivially 1).

Mathematical computation has been engaged for long to get even larger decimal expansions of Pi. While they are on their quest for larger and even larger Pi, one thing to note is that we expect not to find any finite recurrence of repeatable numbers. So whatever the expansion we have so far, there should never be a finite numbers of decimal expansion that repeats itself. If we ever get to a situation like that, Pi would no longer would be qualified as interseting, yet irrational number!. It will degenarate into rational number.

Dedekind also had a way to construct real number, that includes irrational numbers!. Following a similar approach, there is new number system - called surreal numbers.  This has a significant implication in combinatorial games, and artificial intellegence. In most board games, alternate moves of the players creates different positions. These postions can have game values in certain kind of games, and that can dictate the search strategy...