Let S be a subset of the real numbers Claim If t a is limit

Let S be a subset of the real numbers. Claim: If t a is limit point of the set S, then every neighborhood of t contains infinitely many points of S. (a) Write the contrapositive of this sentence: If t is a limit point of the set S, then every neighborhood of t contains infinitely many points of S.

Solution

Answer :

Consider the given statement

\" If t is a limit point of the set S , then every neighbourhood of t contains infinitely many points of S.\"

Then the contrapositive of the above statement is

\" If every neighbourhood of t does not contain infinitely many points of S then t is not a limit point of the set S