How about that Rule your math teacher gave you with warnings to never ignore:  Do Not Divide by Zero!  Why not?  I can multiply by zero, I can divide zero by any number I want, I can put as many zeros after a decimal point with no change to the value of a number, so what’s up with this rule?

English: SpeedCrunch showing a divide by zero error (Photo credit: Wikipedia)

Ask someone why you can’t divide by zero and you’ll most likely get an answer that mentions the fact that you “can’t divide by nothing.”  Well, duh, I can multiply by nothing, so that doesn’t explain it.  How, then, DOES one explain it?

Remember back in 3rd grade when you learned how to divide?  Your teacher taught it as the opposite of multiplication.  Why is 12 divided by 4 = to 3?  Because 4 times 3 = 12!  So try that with division by zero.  If 5 divided by 0 is some number, then it must mean that 0 times that number is = to 5.  Uh, oh, do you see what happens here?  That’s not possible!  Zero’s Special Property is that if you multiply it by ANYTHING you get ZERO (never 5!).  Bingo, you now have the Mathematical reason why you can’t divide by zero; there’s no multiplication fact to check it!

And don’t you feel just a wee bit smarter than you did before you read this?  In my next blog, I’ll show you what can happen if you ignore the rule!

1. I like your answer! Mine would have been, “When you graph Y = N/X, Y approaches infinity as X approaches 0.” Which has lead some to the opinion that division by zero should be legal and equal to infinity. But your way demonstrates that doesn’t work! Infinity times zero = (sorry, guys, still) zero!

2. Also note, though, that you can get something from nothing, in physics as well as math. Matter plus anti-matter=nothing. Nothing=matter plus anti-matter. 5+ -5=0 0= 3.1416+ -3.1416. Etc.

• Mark, I do like your thinking! you say “you can get something from nothing” — worth giving it a try!

• Well, it’s more a philisophical something from nothing. Anyway, I’ve already conjectured that absolute nothingness is impossible. 😉

• Tch, tch… don’t you watch Star Trek? When you combine matter and anti-matter, you get Warp Drive! Engage!! 🙂

• Thanks, Wyrd Smythe. I’ve been watching Star Trek since the early days …. some very interesting math and science ideas generated….I’ll be reading your blog, hope you come back to mine.

• You betcha! Always happy to help (and I love teachers and mathematics). I’ll be looking forward to more of your math posts!

• Thanks again!

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