Functions

Algebra Level 4

True or false :

Let f : N → N f: \mathbb N \rightarrow \mathbb N be a function such that f ( n + 1 ) > f ( f ( n ) ) f(n+1)>f(f(n)) for all natural numbers. Define g : N → N g: \mathbb N \rightarrow \mathbb N as g ( n ) = f ( n ) − n g(n)=f(n)-n . Then, g g need not be well defined.

False True

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1 solution

So, we conclude that g g WILL NOT be well defined.

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what does WELL DEFINED imply

Rohith M.Athreya - 5 years, 3 months ago

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It implies that g(n) is defined for all natural n and g(n) is a natural number.

A Former Brilliant Member - 5 years, 3 months ago

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