"Politically correct" is touted as the correct way to behave. It is not, it's just the way to make Democrats happy. "Mathematically correct" is different. If you are not mathematically correct, the answer is wrong, although it may look right. Here are the mathematically correct principles:

  1. Unless a problem contains a random element or a vague statement, it should always have the same answer.
  2. You can not distribute powers or roots across addition or subtraction.
  3. In set theory, complements can not be distributed across other connectives.
  4. You can't spend money you don't have yet.
  5. Never use multiple-choice questions, unless it is IMPOSSIBLE for more than one answer to be true simultaneously, and it is IMPOSSIBLE for all answers to be false.
  6. For the above reason, multiple-choice must NEVER be used in surveys or elections. A person could favor more than one choice, or none of them. A list of five choices has 243 outcomes, where each choice is given YES, NO, or DON'T CARE as answers. A choose-one multiple-choice restricts the number of available options to 6, and prevents many from voicing their true opinions. More on this.
  7. Tree-type sports playoffs never produce the correct result for any place except first place. The only fair playoff method is a round-robin playoff, where each team plays every other team, on a neutral court.
  8. Rankings are statistical garbage. They must never be used for decision-making.
  9. Never express mass in pounds, dynes, or newtons.
  10. Never express force in grams or slugs.
  11. Weight is a force, not a mass. Weight the force produced by the acceleration of gravity acting on a mass. An object has the same mass on the Earth and on the Moon, but on the Moon it weighs 1/6 what it weighed on Earth.
  12. Celsius and Fahrenheit temperatures cannot be compared quantitatively. They must be converted to kelvins or rankines to be compared.
  13. Never confuse temperature with heat. One 100 watt bulb has a higher temperature, but produces 5/6 of the heat that two 60 watt bulbs make producing the same amount of light.
  14. When counting the number of possible outcomes, find out whether a particular item can occur more than once in an outcome. This affects which counting method you can use.
  15. When counting possible outcomes, find out whether changing the order of items in an outcome makes a different outcome. This affects which counting methods you can use.
  16. Don't let fencepost errors ruin your math. How many posts are needed to hold up a straight rail-and-post fence ten rails long? You are wrong if you said anything other than eleven. Many problems are fencepost problems. A problem involving discrete states and transitions must have one more state than the number of transitions unless circular or bypass paths are possible.
  17. A permanent increase in the rate of government spending causes only a temporary increase in the output of the nation's economy, but causes a permanent increase in the deficit that undoes the increase in the output and eventually reverses it.
  18. You can not prove that something does not exist.
  19. The speed of a car that has crashed can not be found by using the length of the skidmarks alone. The impact shortens them. Also, antilock brakes should leave no skidmarks.
  20. Velocities can not be averaged. The total distance must be divided by the total time.
  21. You can't average averages, unless each average has the same number of items in it. The sum of the items should be divided by the total number of items.
  22. Labor unions argue economics that benefit unions, at the expense of the rest of us.
  23. Movie ticket and recording sales should be compared by number of items sold. The number of dollars must not be used, and rankings must not be used. Otherwise, movies made after inflation are given a definite advantage over movies made before the inflation occurred, because the money changed value. Sales of other items should be similarly compared.
  24. The new millennium begins on January 1, 2001. 2000 is the last year of the current millennium. Yet millions of chowderheads celebrated a new millennium in 2000.
  25. There was no year numbered zero. One B.C. was the year before 1 A.D. (and none of that C.E. stuff! Call it what it means.) The number of years between two dates spanning the B.C. to A.D. juncture must be reduced by one as a result. This happened because Roman numerals were used to create the calendar. There is no zero in Roman numerals. This is why the millennium begins in 2001.
  26. Police RADAR can be fooled. Two large trucks going in opposite directions can cause a higher speed reading than the speeds of any vehicles present. So can the wind blowing briskly through tree leaves. But a driver can't do anything to fool police RADAR.
  27. There are actually 27 standard time zones in the world, even though there are only 24 hours in a day. Three pairs of zones have the same clock time, but are one day apart. There are also some oddball time zones not included in the 27: Central Australia is one half hour off the standard times, and some Middle Eastern countries reset their time every day in step with the sun.
  28. Some computers (e.g. Motorola) use bus speed to determine the advertised clock rate. Others (e.g. Intel) use the clock-crystal speed, even though it is divided down to produce the bus clock. A 200 MHz Pentium actually has a bus speed no faster than 80 MHz. Only the bus speed can be used to compare them directly.
  29. I have found an exact method of trisecting an angle, but it takes an infinite amount of time and infinitesimally exact instruments and eyes.