# Math Help - Set Help

1. ## Set Help

Give an example of a linearly ordered set (L,<) and an initial segment S of L which is not of the form {x | x<a}, for any a in L.

Any suggestions?

2. There is an important difference between $\mathbb{Q}$ and $\mathbb{R}$ that allows you to find initial segments of $\mathbb{Q}$ you cannot write $\{x\in\mathbb{Q}\ ;\ x for any $a\in \mathbb{Q}$.

An example different from the ones you get with the remark: $[-\infty ,0]\subset\mathbb{R}$.