Consider two not equal and positive rational numbers \(\frac{a}{b} < \frac{c}{d}\). The number \(\frac{a+c}{b+d}\) is the **mediant **of the two numbers. It is not hard to verify that \(\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}\).

This was posted to test latex handling of the new setup.