To infinity and beyond

Bedales 6th Form Maths Society’s first topic of discussion this year was infinity! A rather puzzling matter that opened with a discussion about the paradox of Hilbert’s Hotel: a hypothetical hotel with an infinite amount of rooms, which one day became full, much to the annoyance of the holiday makers waiting outside. Hilbert asked every resident to move to the room with the next room number, leaving room one free. But when a tour company sent whole buses of people at a time this created another problem. Hilbert’s solution was to ask all the residents to move into the room whose number was twice that of the room they were in so that all the odd numbered rooms became free. Well done Hilbert!  We then discussed googol (10100) and its larger relation the googolplex (1010)100.These numbers are so massive yet considered small in terms of infinity. Michael left us all with a problem to solve: the St Petersburg Paradox. This is a game of chance where a coin is flipped until it lands on tails; the prize money one is given by £2number of flips. The question asked was how much a casino should charge so it can break even or make a profit?

By Freddie O’Donald, 6.1


Bedales School is one of the UK’s top independent private co-education boarding schools. Bedales comprises three schools situated in Steep, near Petersfield, Hampshire: Dunannie (ages 3–8), Dunhurst (ages 8–13) and Bedales itself (ages 13–18). Established in 1893 Bedales School puts emphasis on the Arts, Sciences, voluntary service, pastoral care, and listening to students’ views. Bedales is acclaimed for its drama, theatre, art and music. The Headmaster is Keith Budge.

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