• Question: What is the weirdest part of maths and why

    Asked by MontyH-S on 15 Jan 2025.
    • Photo: Sheridan Williams

      Sheridan Williams answered on 15 Jan 2025:

      I love the fact that you could find the complete works of Shakespeare in the digits of pi, or e or any trancendental number. (pair numbers so 01=A, 02=B, reduce then to modulo 26 and start searching.
      The longest word I found in 85,000 decimal places of pi was HOTEL, so you’d have to carry on producing digits beyond the life of the universe!

Comments

  • Photo: Edward

    Edward commented on :

    One good area to explore is the concept of infinity and how weird it is. To begin, let’s say we have two groups, {1,2,3} and {a,b,c}. We might not know exactly how big they are, but if we can match up their contents in a 1 to 1 relationship, we can say they are the same size. We can match them like this … 1-a, 2-b, 3-c.
    Now comes some weird stuff…. let’s take the set of natural numbers {1,2,3,4,…} and the set of even numbers {2,4,6,8,…}.
    It looks like the set of even numbers must be smaller than the set of natural numbers because the set of natural numbers contains all odd numbers as well as even numbers. But, consider this…
    I will define a 1-1 matching between the two sets as follows … n to 2n.
    So for any natural number, I can define exactly one even number by multiplying by 2 and for any even number, I can define the natural number matched to it by dividing by 2.

    This is really weird. In fact, we can repeat this by showing the set of all square numbers {1,4,9,16,… } is the same size (or cardinality) as the set of natural numbers. We can also do the same for the set of fractions.
    BUT… we CANNOT do this for the set of real numbers. Real numbers contain all the integers, fractions and numbers such as Pi and e. This means there is a second, larger infinity!
    For more on this, you can do a google search for ‘Hilberts hotel infinity’.