>>2062
Well, my earlier argument implicitly assumes x and y are finite numbers.
Infinity + Infinity = Infinity and Infinity + x = Infinity (where x is a finite number)
Also, Infinity/x = Infinity (where x is finite and not zero)
So if x and/or y are infinite, then:
average(x,y) = Infinity
average(x,x,y) = Infinity
Therefore average(x,y) = average(x,x,y) in this case.
In particular, if x = Infinity and y is some finite number, then you have a counterexample.
However, a lot of stuff we take for granted breaks down when infinity is involved. It is often assumed implicitly that infinity is not allowed for this reason. That said, it's not a problem to consider what happens when infinity gets involved.
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