Starting with the number 0 on my calculator, I do a calculation in five steps. At each step, I either add 1 or multiply by 2. What is the smallest number that cannot be the final result?
do you HAVE to add 1 at least once?
otherwise you just multiply 2 five times and that is the least because there is no way to get a negative number.
If you do,
then try to avoid multiplying by 2 AFTER you added 1.
If you multiply by 2 five times then you get 0
So the biggest interger on the too little side that you cannot get it -1. The smallest is - infinity. (but that is not an integer)
Of course numbers do not have to be integers, they do not even have to be real, so the question should have been better stated.