Why Can't You Divide by Zero? (A Warship Found Out)

Step by step

1. A warship stopped · a computer divided by zero
   A US Navy warship stopped dead in the water. The reason? A computer divided by zero.
2. 6 ÷ 0 = ? Zero? Infinity? Something else?
   So what is six divided by zero? Zero? Infinity? Something else?
3. Try 6 ÷ 0 on your phone. What does it show?
   Try it on your phone's calculator. What does it show?
4. 6 ÷ 2 = 3 because 3 × 2 = 6
   Here's the key. Division undoes multiplication. Six divided by two is three, because three times two is six.
5. ? × 0 = 6 · but anything × 0 = 0
   So six divided by zero asks: what number times zero is six? But any number times zero is zero. Never six. There's no answer.
6. 6, 60, 600 … up forever
   Then is it infinity? Divide six by smaller and smaller numbers: six, sixty, six hundred. It shoots up forever.
7. From the other side: down forever
   But come from the negative side: negative sixty, negative six hundred. It shoots down. The two sides never meet, so there's no single answer.
8. 0 ÷ 0: every number × 0 = 0 → no single answer
   And zero divided by zero? Every number times zero is zero, so every number works. That's no single answer either.
9. Dividing by zero is undefined
   So the rule: you can't divide by zero. It's undefined.
10. 628 Brahmagupta vs 1100s Bhaskara II
    Great mathematicians argued about this. In six twenty-eight, Brahmagupta wrote that zero divided by zero is zero. About five hundred years later, Bhaskara the Second called a number divided by zero infinite.
11. JavaScript: 6 / 0 → Infinity · math: undefined
    And today, some programming languages, like JavaScript, print Infinity for six divided by zero. That's a computer convention. In math class, it's undefined.
12. USS Yorktown, 1997 · check the divisor first
    Back to the warship. In nineteen ninety-seven, the USS Yorktown's software got a zero and divided by it. The program crashed, the network went down, and the engines stopped. That's why programmers always check: is the divisor zero?
13. On a test: q × 0 = 6 but q × 0 = 0 → undefined
    On a test: suppose six divided by zero is some number q. Then q times zero is six. But q times zero is zero. Zero can't equal six, so six divided by zero is undefined.