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About lim inf and lim sup

  1. Nov 25, 2014 #1
    1. The problem statement, all variables and given/known data
    Demonstrate lim inf an × lim inf bn ≤ lim inf (an × bn)

    2. Relevant equations


    3. The attempt at a solution
    Fixxed n € N , n≤ k , inf ak ≤ ak , inf bk≤ bk =》inf ak × inf bk ≤ (ak × bk) . Being inf ak × inf bk ≤ any element from {ak} × {bk} it`s logical that inf ( ak × bk ) ≥ inf ak × inf bk... the part i don't get it's the following: the teacher suddently writes : sup inf ( ak × bk ) ≥ sup inf ak × sup inf bk.. the part after this is much easier since sup inf ak = lim inf an , sup inf bk = lim inf bk and sup inf ( ak × bk ) = lim inf ( ak×bk)
    Can anyone solve this mistery? Many Thanks in advance
     
  2. jcsd
  3. Nov 26, 2014 #2
    Canany mentor delete this post? I just discovered how it works and i should be fine
     
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