Rudin, Principles of Mathematical Analysis, Chapter 2 Exercises

Problem 2.1. Prove that the empty set is a subset of every set.

Solution. Given any set $A$, we need to show that $x \in \emptyset$ only if $x \in A$. As the empty set contains no elements, this condition is vacuously satisfied, hence $\emptyset \subseteq A$.

No comment found.

Add a comment

You must log in to post a comment.