You may have once seen a "proof" that you never go to school (or work), all appearances to the contrary notwithstanding. It might have gone something like this:
- There are 365 days in a year.
- But you don't go to school on Saturdays or Sundays; there are 104 of these, so 365−104 = 261.
- You don't go to school on summer vacation either; the length of summer vacation varies, but say that it's 68 days long, so 261−68 = 193.
- You also get Christmas vacation off, which is 16 days long; 193−16 = 177.
- You also get March break or spring break off, which is 9 days long; 177−9 = 168.
- School doesn't last all day though; maybe you have 8 40-minute classes each day, so 168 × 8 × 40/60 = 896 hours.
- However, most jurisdictions have about 12 statutory holidays each year, and you don't go to school at all on those days; 896−12×24 = 608.
- There are also a few (say, five) professional development days in the school calendar, so 608−5×24 = 488.
- Of course, there are some days you don't go to school at all, either because you're sick or you have an appointment or your parents took you somewhere or you didn't want to go. Say there are five such days each year. 488−5×24 = 368.
- While you're at school, you probably get about an hour every day for lunch and/or recess; 368−365 = 3.
- The first day of school is usually a half day, so subtract 3 hours: 3−3 = 0.
- Therefore, you don't go to school at all.
But (assuming you're a student) you do go to school, so what's gone wrong? The problem is that a lot of times when you don't go to school are counted multiple times. For example, a summer Sunday is subtracted when accounting for Sundays and again when accounting for summer vacation.
The above was just for fun, but there is a real world lesson to be learned here. Sometimes you'll see in the news some claim that shoplifting, or mental illness, or goofing off on the Internet at work, or something else costs some enormous sum of money, or that some new government spending programme will create some enormous number of jobs. You can probably bet that, just like the example above, there was a lot of counting things twice, three times, or even more.
See also logical fallacies and mathematical fallacies.