Prove or Disprove Let S be an infinite set Then there is a s

Prove or Disprove. Let S be an infinite set. Then there is a set A subset S such that A is equinumerous to N.

Solution

Since S is an Infinte set,and A is the subset of \"S\" so there is a possibility that subset \"A\" may also have infinte set,

also set of Natural numbers i.e. set \"N\" is also an Infinite set so cardinality of both set \"A\" and set \"N\" are infinite so

both set would be equinumerous to each other.