The Set Theory Test
Their result for The Set Theory Test ...
Very smart
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)
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They scored 58% on Axioms, higher than 43% of your peers.
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They scored 56% on Fundamentals, higher than 40% of your peers.
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They scored 45% on History, higher than 31% of your peers.
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They scored 57% on Application, higher than 44% of your peers.
All possible test results
Average Joe/Jill
You don't seem to have an understanding of set theory all that much. You're the average non-mathematician. You might have gotten some questions right just by using your common sense -- good for you.... Read more
Smart, not informed
You don't know your axioms all that much, but you're good with your fundamentals. And it's the fundamentals that count! You're average if you've studied set theory before. But if you haven't... Read more
Odd genius
You're a genius! You have the fundamentals down. But you have no idea about the axioms. And that's okay. Because, it's the fundamentals that count! If you haven't studied set theory ... Read more
Book smart
You know your rules and axioms. But you don't understand the fundamentals at all! I'm sorry to say this, but set theory isn't for you (i.e. you'd never really get into set theory). But I'm sure you... Read more
Very smart
You're very smart. You have your axioms down and you've done pretty well on your fundamentals too. If you haven't studied set theory before, you are very gifted and set theory is your call... Read more
Genius
Genius! You have your axioms down and you've done great on your fundamentals too. If you haven't studied set theory before, are not only very gifted but are the next big mathematician... a... Read more
