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'Indexing Problems' printed from https://nrich.maths.org/
Constructing a really clear argument to this problem can be
difficult!
Put simply:
Suppose that exactly one of the following statements is true:
A: Ultra Ref does refer to itself in its index
B: Ultra-Ref does not refer to itself in its index
Look at each in turn:
IF (Ultra-Ref does refer to itself in its index) THEN (Ultra-Ref
does not refer to itself in its index)
IF (Ultra-Ref does not refer to itself in its index) THEN
(Ultra-Ref does refer to itself in its index)
In both cases, our supposition is contradicted and Ultra-Ref is
therefore a logical impossibility.