An interesting bijection
Level
pending
Let f be a bijection from [0,1] to the real numbers. Which of the following statements must be true? Note: pick the strongest statement if you think more than one of them are correct.
f exists and can be continuous.
Such f doesn't exist.
f exists and can have only finitely many discontinuities (at least one).
f exists and must have infinitely many discontinuities.
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