Questions asked by roman a.

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• How do I prove that this limit is equal to 1 in a formal way ? (without using l'hospital rule)
  
• Anyone can explain to me what's the difference between "limit", "limsup" and "liminf" of a function? It would be helpful to explain with concrete example.
  
• Is that true to say: For every set A defined by A={ A : ∅∉A } then the Cardinality of A equals to |A|-1 ?
  
• How do I prove that the limit of this function is #1/n#? (#n# is a positive integer)
  
• Which values of x this function is continuous? (x non-negative real number and n->infinity)
  
• What the difference between cardinality and dimension of a set? for example for R^3 and R^n.
  
• How can the set {(1,0,0), (0,1,0)} span R^2 when you have 3 coordinates in each vector?
  
• Let V be a vector space over F. Explain why we can think of V as a vector space over K ( K subset of F)?