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.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Here on page 232-233 the author offers a proof of the Bernstein-Schroeder Theorem. He uses the subset

$$\bigcup_{k=0}^\infty(g\circ f)^k(A-g(B))\subseteq A$$

and I'm not exactly sure how to parse this. Does this mean the union of the powers of the composition $g\circ f$? If so how is this a subset of $A$? I'm having a bit of trouble seeing it.

share|cite|improve this question

It seems like you have the right interpretation. Notice that $g\circ f$ is a function sending $A$ to $A$, and therefore so is $(g\circ f)^k$ for all $k$.

share|cite|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.