Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For a collection, $A$ of subsets of a set $X$ to be an algebra of subsets it must satisfy the following properties:

  1. $A$ is non-empty
  2. If $E \in A \implies E^c \in A$
  3. If $E, F \in A \implies E \cup F \in A$

However in other sources I have seen an algebra of subsets presented as:

  1. $\emptyset, X \in A$
  2. If $E \in A \implies E^c \in A$
  3. If $E, F \in A \implies E \cup F \in A$

The first property in each definition does not seem equivalent to me. So is the definition of an algebra of subsets non-standard, i.e. it varies depending on the author of the text?

share|improve this question

1 Answer 1

up vote 4 down vote accepted

Well, if $E\in A$ then $E^c\in A$ so their union which is $X$ is in $A$ and and so is their intersection which is $\varnothing$.

So being non-empty is equivalent to having $X$ and $\varnothing$ in $A$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.