check that a series of time periods in a weekly schedule don't overlap

def overlaps(periods):
    sorted_by_lower_bound = sorted(periods, key=lambda tup: tup[0])
    for higher in sorted_by_lower_bound:
        for lower in sorted_by_lower_bound:
            if higher[0] < lower[1] and higher != lower:
                return True
    return False

overlaps([(1, 3), (2, 4), (4, 5)])