- #1

cooljosh2k2

- 69

- 0

## Homework Statement

Show that if a ∈ R, then:

sup{r ∈ Q : r < a} = a .

## The Attempt at a Solution

Seems like a very simple question, but the r is throwing me off. Do you prove it the same way as a natural number using an epsilon? For example:

If a is an upper bound of S and if v < a, then we put ε = a - v... etc.

or is there a different way to prove a supremum with a rational number.