You should be able to solve this.

Create a method to choose a random integer between 0 and infinity such that no integer is more likely to be chosen than any other.

Yes it is possible, I don't care what your probability book says (Notice I didn't even use the word "probability").  You may assume the axiom of choice.

Another one

x/0=y, where y is the random integer

anything divided by 0 can be anything because any number of 0s fits into 0