I was offered a problem in which you were given four 9's like this:
9 9 9 9
And by adding mathematical functions (+, -, /, *, floor/ceiling, log, ln, trig, factorial) you could make it sum to the numbers 1-100.
Which made me think: Given a positive integer \(n\), how many integers can you achieve from using some sequence of these mathematical functions -- can you get all of them? Only positive integers? I have a feeling that you can get at least every positive integer, but I don't have the evidence to prove it.
What are your thoughts?