Answer as many questions as you can. BE AS BRIEF AS POSSIBLE but not too brief. You do not need complete sentences. There is not enough time nor space to write complete sentences.

1. Name the three schools of thought that arose to address the problem of the foundations of mathematics in the early 20th century.
2. How do set theory and type theory differ in their relationship to logic?
3. In mathematics, objects ________________, but in computer science, objects ________________.
4. Distinguish cardinals and ordinals.
5. Arrange integers, naturals, rationals, computables, reals, describablles, and algebraics in order of increasing cardinality.
6. According to Vi Hart, $81^{\frac{3}{4}}$ is what exactly? (Hint: Start your answer with "Counting three- ..." and finish it with "sort of way".)
7. Unsugar $(2, 5, 8, 3, 1)$
8. Is the less-than relation on numbers asymmetric, antisymmetric, both, or neither? This is a timed exam, so if you don’t know, save this until the end, and if you still don’t know, just guess.
9. Write, in lambda notation, the function to pentate 3 by the argument of the function you are writing.
10. Write, in lambda notation, a function that returns the log-base-$m$ of the $n$-fold iteration of the function $f$ starting at $x$. Start your answer with $\lambda m. \lambda n. \lambda f. \lambda x.$