MIT Assignment

Question

f(n) = O(g(n)) and g(n) = O(f(n)),then f(n) = g(n) ---> True or False

The answer to this question is False and this the explanation given by them  " False: f(n) = n and g(n) = n+1".

Someone please explain what are they trying to say.

Comments

If two functions are asymtotically equal,that does not mean they are mathematically equal.Can this be inferred ?

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Yes correct, lets take

f(n) = n+6

g(n) = n+3

Both are mathematically unequal

But both are  of O(n)

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All the confusion in this is because of mathematical and assymptotically equivalence. They are assymptotically equal but not mathematically.

You can refer Anand's explanation for more clarification. He did it perfectly.