traps · logic
1 = 2
The steps use a = 1 and b = 1.
These steps start from 1 = 1 and arrive at 2 = 1. Which step is not allowed?
- 1 a = b 1 = 1
- 2 a2 = ab 1 = 1
- 3 a2 − b2 = ab − b2 0 = 0
- 4 (a − b)(a + b) = b(a − b) 0 × 2 = 1 × 0
- 5 a + b = b 2 = 1
a and b are both 1. Pick the step that is not allowed.
Both sides were multiplied by 0. Crossing that factor out is dividing by 0, so the step is not allowed. 2 = 1 does not follow.
Every earlier line is true for the number 1. The two sides on those lines really match.
The last line is only what you get after dividing by 0. It is not a true result.