i was wondering if you could solve this problem for me: Show that sup({1-1/n: n element of Natural numbers}) = 1

Question

discrete mathematic

Answer 1

You can prove it by contradiction.

Suppose there is another least upper bound T , not equal to 1,such that

 

1-1/N < T< 1 for n=1,2,3,....

Taking the limit as n tends to infinity of all three sides forces T =1 by sandwich theorem.