Should I feel bad for applying to two postdoc positions? I'm a finishing PhD student in math. I want to stay in academia so I am applying for two things:


A year-long postdoc position
A 6 month postdoc position


I have been in contact with two professors regarding the two options and am going to send the application forms off today. But I feel bad because suppose I get job offers for both the positions, then I'll have to say no to one of them. Then they will get annoyed at me for wasting their time and will probably never want to work with me on anything again. Both are highly respected so it's doubly bad. What should I do?

Edit: the applications will be decided by a committee, not the professors concerned. Both professors are happy to work with me. I'm in the United Kingdom.
Everyone who is hiring knows that applicants are applying for multiple positions. This covers everyone from McDonald's to Harvard. It's expected. They will get multiple applications and will only take one, so you must apply to multiple positions to have a chance of landing one. Unless you have an offer in hand which you have already accepted when you apply for another position, you haven't done anything wrong. I'm surprised you've only applied to two.