Monday, October 13, 2008

This whole 9=8 thing...

From an interesting read by Yahoo's Jeff Passan:

This proof, provided by Michigan State assistant math professor Ignacio Uriarte-Tuero, would seem to prove that, in fact, nine does equal eight, as Tampa Bay Rays manager Joe Maddon has asserted all year.

It doesn’t, of course, as nine can’t equal eight. Though the error is difficult to spot. Can you find it?

Step 1: Let x = y. Multiply by y to get
xy = y2

Step 2: Subtract x2 to get
xy − x2 = y2− x2

Step 3: Factoring, we get
x(y − x) = (y − x)(y + x)

Step 4: which simplifies to
x = y + x

Step 5: and now using that x = y we get
x = 2x

Step 6: Simplifying again, we get
1 = 2

Step 7: so that when we add 7 to both sides we get
8 = 9

Step 8: or put in other words,
9 = 8

And if it hasn't already been brought to your attention, the Rays won Game 2 of their series 9-8, in 98 innings, in the 98th year of Red Sox baseball, at precisely 9:88 p.m. on the 9th of 8 with 9 men on an octagonal field...

For my money, Phillies-Dodgers has proven the more interesting series. Last night Russell Martin got hit again (twice!), while Dodgers pitcher Hideki Kuroda -- who looked like a dead-man walking the next half-inning, dreading what he had to do -- threw a ball above Shane Victorino's head in retaliation, prompting, after getting Victorino to ground out to first, a bench-clearing staredown. If this, my friends, were a mystery novel, we'd say Game 3 has moved us out of the exposition. And soon, the murder.

1 comment:

  1. Between Step 3 and Step 4, he is dividing both sides by (y-x). In this case, y=x, so then y-x = 0. You are not allowed to divide by zero, so this is an undefined operation, and the "proof" breaks down at Step 4.