I was studying Probability today, I found this interesting table in Oliver Knill's book on probability
I thought this was a nice summary of different set algebras collected in one place. I had never thought of typologies and Borel sigma algebras as other type of set algebras!
I tried to make sense of when and why each was used, but I could not really find a good reason to prefer some systems over another. They appear to be more or less useful depending on contexts.
Importantly, it reminds me that as much as I find the structure of mathematics elegant, somehow the foundations are specified so that things are built to work.
I thought this was a nice summary of different set algebras collected in one place. I had never thought of typologies and Borel sigma algebras as other type of set algebras!
I tried to make sense of when and why each was used, but I could not really find a good reason to prefer some systems over another. They appear to be more or less useful depending on contexts.
Importantly, it reminds me that as much as I find the structure of mathematics elegant, somehow the foundations are specified so that things are built to work.
