## Wednesday, 18 July 2012

### True or False...?

I brought this up at school today and it created quite a bit of discussion.

True or False:

If xa = xb  then a = b.

I'll do a full post on this once I have some answers.

Emma x x x

1. False. Counter-example available on request :-p.

1. Thanks for starting the ball rolling Adam! But remember folks, he might not be correct, so don't worry if you disagree with his answer! That "counter-example", valid or not, will feature in the next post. Thanks!

1. Oh good, we have a clash of opinions! I do love to maths debate. :-)

2. You just had to get that in, didn't you...?

Anyway, it's false.

3. I couldn't resist!

Can you give me an interesting counterexample?

2. Counterexample: 0^1 = 0^2 but 1 ≠ 2

1. Congratulations anonymous, you've managed to come up the most boring counterexample EVER! But I suppose it is valid, so well done! :-)

Can anyone come up with a less trivial counterexample?

3. e^0 = e^(2*pi*i) = e^(4*pi*i) = etc ( = 1)

4. Beautiful!