The ages of young star clusters, massive blue stragglers and the upper
  mass limit of stars: analysing age dependent stellar mass functions
  Massive stars rapidly change their masses through strong stellar winds and
mass transfer in binary systems. We show that such mass changes leave
characteristic signatures in stellar mass functions of young star clusters
which can be used to infer their ages and to identify products of binary
evolution. We model the observed present day mass functions of the young
Galactic Arches and Quintuplet star clusters using our rapid binary evolution
code. We find that shaping of the mass function by stellar wind mass loss
allows us to determine the cluster ages to 3.5$\pm$0.7 Myr and 4.8$\pm$1.1 Myr,
respectively. Exploiting the effects of binary mass exchange on the cluster
mass function, we find that the most massive stars in both clusters are
rejuvenated products of binary mass transfer, i.e. the massive counterpart of
classical blue straggler stars. This resolves the problem of an apparent age
spread among the most luminous stars exceeding the expected duration of star
formation in these clusters. We perform Monte Carlo simulations to probe
stochastic sampling, which support the idea of the most massive stars being
rejuvenated binary products. We find that the most massive star is expected to
be a binary product after 1.0$\pm$0.7 Myr in Arches and after 1.7$\pm$1.0 Myr
in Quintuplet. Today, the most massive 9$\pm$3 stars in Arches and 8$\pm$3 in
Quintuplet are expected to be such objects. Our findings have strong
implications for the stellar upper mass limit and solve the discrepancy between
the claimed 150 $\mathrm{M}_\odot$ limit and observations of fours stars with
initial masses of 165-320 $\mathrm{M}_\odot$ in R136 and of SN 2007bi, which is
thought to be a pair-instability supernova from an initial 250
$\mathrm{M}_\odot$ star. Using the stellar population of R136, we revise the
upper mass limit to values in the range 200-500 $\mathrm{M}_\odot$.
