Given a sorted ascending sequence of fractions, if I add a constant $c$ to each fraction's numerator and denominator, how is the sequence affected?
For example, if I have a sequence in ascending order:
$\frac12, \frac38, \frac57, \frac ab,\ldots$
if I add a constant $c=1$
$\frac{1+c}{2+c}, \frac{3+c}{8+c}, \frac{5+c}{7+c}, \frac{a+c}{b+c},\ldots$
will my sequence still be sorted in ascending order?
Thank you!