# Fizz Buzz For Mathematicians

It's well-known (for some definition of "well-known") and deeply controversial that 80% (some say 90%) of applicants for programmer jobs can't actually program[0][1]. Recruiting good programmers (for some definition of "good") is a known "Hard Problem(tm)"

To this end an initial "bozo-filter" is sometimes applied, wherein a candidate is asked to write some utterly trivial code to demonstrate that they have at least a basic grasp of how to write programs. A common test is the "FizzBuzz" test - go look it up.

So I was idly speculating - what would be a similar initial filter for "Mathematician"? This is clearly an impossible question, because we don't actually know what a mathematician is, nor do we really know what a mathematician does. However, we don't actually know what programmers do either, so maybe that's OK.

One possibility that came to mind is this question:

• An "equivalence relation" on a set X is a function

$E:X{\times}X\rightarrow\{T,F}$
that satisfies these three conditions:
• For all x in X, E(x,x)=T,
• For all x and y in X, E(x,y)=E(y,x),
• If E(x,y)=T and E(y,z)=T, then E(x,z)=T.
• Suppose E(x,y)=F and E(y,z)=T. What can you say about E(x,z) ?
• Prove it.
Problem is, I wonder if too many non-mathematicians can pass this test to make it of any value.

Can you?

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