The Set U: Proving Non-Emptiness and Upper Bound

[silvermane]

Homework Statement

We have U = { 3n/(n+1) : n in N }

i. Prove that U is non-empty and bounded above by 3.
ii. Prove that if a is a real number with a<3, then there is an n in N such that a < 3n/(n+1)

The Attempt at a Solution

i. We can show it non-empty by saying that 3/2 is in the set since 3*1/(1+1) = 3/2, but I'm a little confused in how to prove that 3 is an upper bound, and that a is smaller than our equation. :(

I don't want answers, but hints and tips are greatly appreciated ))

 

[╔(σ_σ)╝]

n/(n+1) < 1

 

[HallsofIvy]

n/(n+1) < 1

Well, if you want to do it the easy way!

I was all set to do a proof by induction on n!

To get the last, that if a< 3 then there exist an integer n such that a< n/(n+1), try solving for n.

 

[╔(σ_σ)╝]

Well, if you want to do it the easy way!

I was all set to do a proof by induction on n!

To get the last, that if a< 3 then there exist an integer n such that a< n/(n+1), try solving for n.

XD.

Are you sure you don't want to use some complex analysis ? :p