Maths question

• c0mplex

  31 Jan 06, 10:55

  If {a_n} converges to L, does it mean that |{a_n}| also converges to |L|? If yes, why?
• nukewatch

  31 Jan 06, 11:11

  Originally posted by c0mplex:

  If {a_n} converges to L, does it mean that |{a_n}| also converges to L? If yes, why?

  If L < 0, how does |{a_n}| converges to L?
• c0mplex

  31 Jan 06, 11:23

  ops... should be |L|... sorry for the typo
• greengoblin

  31 Jan 06, 12:15

  Use triangular inequality. If you are doing real analysis, this should be a standard weapon in your arsenal.
• c0mplex

  31 Jan 06, 12:19

  i tried... but don't know how to continue...
• greengoblin

  31 Jan 06, 12:24

  Go and prove
  ||{a_n}| - |L|| < |{a_n} - L| < e
• c0mplex

  31 Jan 06, 12:31

  ahh..... i know how le... i keep thinking about the 'normal' triangle inequality... i forgot about the reverse triangle inequality... thanks