Order 7 of the following sentences so that they form a logical direct proof of the statement:

[math]

Choose from these sentences:
  1. Assume [math]
  2. Assume [math] and [math]
  3. There is no limit.
  4. [math]
  5. Choose [math] so that [math] and [math].
  6. Then [math]
  7. [math]
  8. Therefore, [math]
  9. [math]
  10. Use Wolfram-Alpha to figure this out.
  11. Assume [math].
  12. Suppose [math]
Your Proof: