Would one catch hiv/aids from a razor blade cut?

Depends: Chances of getting HIV virus or aids from a sterile blade or new blade is zero. The chance of getting virus through an infected blade that was used previously by a person with hiv/aids although very low is still present. It is recommended in general to not share razor blades as most people are not aware of them being infected with hiv. Casual sex with either male or female partner can be lethal.

Unlikely: Unless blade is contaminated with HIV containing blood ; you cut your skin whilst shaving with it.

Yes and no: Keep in mind that to infect someone there 1-has to be HIV virus, 2-enough virus to transmit infection and 3-have an entry into another human. So..Having said this..Technically speaking yes its possible. Has there been documented cases..Not to my knowledge. Other viruses like hep c is far more likely to be spread like that. Remember the HIV virus dies rather quickally outside the bloodstream.