• Question: What is your opinion on infinite series?

    Asked by secretsaudience16 to Sophie, Sam, Andrew on 7 Jan 2020.
    • Photo: Samantha Durbin

      Samantha Durbin answered on 7 Jan 2020:

      I could go on and on, but…

      (sorry, couldn’t resist)

      I remember having a bit of a ‘mind blown’ moment at university when I found out that there are different sizes of infinity (there are infinitely many fractions and infinitely many decimals, but there are far more decimals than fractions – it’s a bigger class of infinity). These days I see others do full 2.5 hour workshops on infinity and you can almost see the students brains stretching, it’s great – one of my favourite Masterclasses (done by someone else) is on infinity. I also look at things like fractals in the sessions I do, which link to infinite series and patterns. Good topics to look up for more info are Cantor’s Diagonal Argument and Hilbert’s Hotel.

Comments

  • Photo: Diana

    Diana commented on :

    They ARE interesting. Particulalry that some series of decreasing fractions have finite limits, other not. they are related ot other objects such as pi, exponent e that are non-rational. Pythagoras knew that √2 was irrational – some say he was so upset at discovery of irrationals he committed suicide. for othere such as Cantor and Erasthones these wierd facts, only discoverable by maths, were inspirationla

  • Photo: Maja

    Maja commented on :

    I love them!
    It’s especially cool that some of them sum to infinity and some into a function (for example exponential function).