- #1

jr16

- 14

- 0

## Homework Statement

For the following set if it has an upper bound, find two different upper bounds as well as the least upper bound (LUB), justifying your answer. If the set has no upper bound, state this and justify your answer.

{x | 1 < x < √(7) and x is irrational}

(a proof requires the density of the irrationals)

## Homework Equations

density of the irrationals theorem

## The Attempt at a Solution

I stated two upper bounds as √(10) and √(37)

But where I get confused is with the LUB. Isn't it simply √(7)? Why does the question state that a proof using the density of the irrationals is necessary?

Had x been declared as rational then this would be more clear to me, since there would be no LUB and I would need to prove this using the density of the rationals.

Where am I going wrong?