Maths All Around

Why is Membership a hot topic?

• We talk about `membership' and `belonging' in life. Membership of the club or the gang or the team.
  Being a passport holder. Belonging (or not) to the group. Classes of things, to which certain things belong.
  Sameness and difference within a group. A notion of "shared ownership".
  
• If a US president says: ``America first.'' - what does it mean?
  

• So, the idea of membership leads us to the idea of (in)equality!
• And... to racism, and sexism.

• And also to ideas of solidarity and cooperation.
• What about membership of the European Union, and Brexit?

• Membership changes our notion of equality!
  Under the laws of membership of a society, a 2m tall man and a 1m tall child might be considered equal.
  But of course 2m is not equal to 1m.
  And they would probably not be considered as equal contributors to a rugby team!
  (Less dramatically, sometimes the symbols A and a can be considered equal - they are both the same letter of the alphabet - and sometimes not.)
  

• Trying to make an informal idea of membership more precise often helps us to organise our thoughts.
  

   

• Maths, of course, has its own versions of membership:
  If a number is an odd number then it is not an even number.
  If an animal is a dog then it is not a cat.
  Exercise: what does this mean? Discuss!
  

4. When membership goes pearshaped

• The set of all sets of size 1. Is this really a set?
  Here are some elements of this `set': The set of people you know for sure exist, {1}, {2}, {3}, {A}, {B},
  {{1}},
  ...No wait. What happened there? (Discuss.)
  {{{1}}},
  For each set, the set containing just this set as an element.
  [Cue Twilight Zone theme tune....]
  The set of people who understood that cultural reference.
  

(back)