Their result for The Set Theory Test ...
58% axioms, 56% fundamentals, 45% history, 57% applications
If you haven't studied set theory before, you are very gifted and set theory is your calling. If you start studying it, it'll change your life.
If you have studied set theory before, you are a good mathematician.
Here are some things that you might have gotten wrong:
- Sets can only contain other sets. It is a general misconception to think that sets can contain any arbitrary object. The reason a set can contain numbers is that each number is defined using a set.
- There are many statements in set theory that can't be proven or disproven. It's easy to make a statement like that using self-referencing. Statements similar to "I'm a liar," can never be true or false.
- We don't know whether set theory contradicts itself or not. But what we do know is that set theory isn't powerful enough to be used to prove/disprove its own consistency (proof of this theory was done by Kurt Goedel).
- The set of all sets does not exist. Axiomatically, of course.
- An axiom is an unprovable assertion.
Their Analysis (Vertical line = Average)
They scored 58% on Axioms, higher than 46% of your peers.
They scored 56% on Fundamentals, higher than 43% of your peers.
They scored 45% on History, higher than 33% of your peers.
They scored 57% on Application, higher than 46% of your peers.
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