Set theory doesn't tend to get used much these days. Initially it was perceived to be a way of explaining everything but that was shot down by Bertrand Russell.
In essence Russell proposed "the set of all sets that do not contain themselves as a member." As you can see set theory breaks down because that set can't contain itself, whilst if it doesn't it must.
In essence Russell proposed "the set of all sets that do not contain themselves as a member." As you can see set theory breaks down because that set can't contain itself, whilst if it doesn't it must.