I was preparing for the GRE exam, and was wondering what the difference was between a premise and an assertion. Any example which highlights the difference would be immensely helpful (something I haven't been able to find online).
Yes, they do seem very similar in that they are both related to 'assumption' or 'axiom' in an argument. You can read their dictionary definitions which will tell you what each are but it doesn't tel you what is important in the comparison.
A 'premise' is an assumption that is usually discovered, implicitly understood, or passively waiting (possibly even hiding), found by working backwards in an argument to a starting point.
An 'assertion' is an actively stated starting point, one made to eliminate there possibilities in forming an argument.
Both, like 'assumption' or 'axiom', are the starting points or base data of an argument, One may question all of these but for the validity of the argument one is expected to accept them as given. One may alter them but then that's a different situation for the argument.