9 = 8

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

There is an error in this proof, obviously...but I couldn't find it....can you??