Using Pythagoras' theorem, it is easy to see that the second term is strictly contained between -1 and 1. Thus 
and it follows that 
is strictly increasing.
. Using (5), it follows that
which, once substituted under the square root, shows that indeed we have 
.
has already been shown when proving 1). To show that is a strictly increasing function, it suffices to show that the second derivative of is strictly positive. The details of this proof are left as an exercise for the interested reader.
.
. This means that for large v/c ratios, t
