def appropriate_number(user_input, lower_limit=1, upper_limit=10):
    """Returns true if user input is a number that is bigger than or equal to
    the lower limit and smaller than the upper limit. Returns false otherwise.
    """
    try:
        a = int(user_input)
        if a < lower_limit:
            return False
        elif a >= upper_limit:
            return False
        else:
            return True
    except ValueError:
        return False