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**Tiberius** · February 12, 2010 at 2:50 pm

Which line contains the fallacy in this mathematical proof?

1. Let a and b be equal non-zero quantities.
a = b

2. Multiply both sides by a.
a2 = ab

3. Subtract b2.
a2 - b2 = ab - b2

4. Factor both sides.
(a - b)(a + b) = b(a - b)

5. Divide out (a - b).
(a + b) = b

6. Substitute a = b.
b + b = b

7. Simplify.
2b = b

8. Divide by b.
2 = 1

Warning!!! Answer:

BioLogos · February 12, 2010 at 2:54 pm

(February 12, 2010 at 2:50 pm)Tiberius Wrote: Which line contains the fallacy in this mathematical proof?

1. Let a and b be equal non-zero quantities.
a = b

2. Multiply both sides by a.
a2 = ab

3. Subtract b2.
a2 - b2 = ab - b2

4. Factor both sides.
(a - b)(a + b) = b(a - b)

5. Divide out (a - b).
(a + b) = b

6. Substitute a = b.
b + b = b

7. Simplify.
2b = b

8. Divide by b.
2 = 1

Very famous and illuminating example. Smile

**Rhizomorph13** · February 16, 2010 at 1:03 am

Line six

**Tiberius** · February 16, 2010 at 3:11 am

What's wrong with line 6? It's a substitution, and since a = b you can substitute it fine.

**theVOID** · February 16, 2010 at 3:28 am

Line 5 is divide by 0?

**Tiberius** · February 16, 2010 at 3:34 am

Well done

**theVOID** · February 16, 2010 at 3:36 am

(February 16, 2010 at 3:34 am)Tiberius Wrote: Well done

It only took 1 and a half a4 pages of scribbling to work it out Tongue

**Tiberius** · February 16, 2010 at 3:37 am

Now I have to find another problem. Grrr. Big Grin

**theVOID** · February 18, 2010 at 6:07 pm

Give me a heads up, i need to go buy more pad paper for working them out.

chris · March 23, 2010 at 4:45 am

(February 12, 2010 at 2:54 pm)BioLogos Wrote: 1. Let a and b be equal non-zero quantities.
a = b

Actually line 1 assumes that both non zero numbers are the same number, line 1 should read:
1. Let a and b be equal non-zero quantities.
a > b or a < b.
This then changes the rest of the proof :-)

All the best

Chris

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