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

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!

true

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

You just had to get that in, didn't you...?Anyway, it's false.

I couldn't resist!Can you give me an interesting counterexample?

Counterexample: 0^1 = 0^2 but 1 ≠ 2

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?

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

Beautiful!

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

ReplyDeleteThanks 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!

Deletetrue

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

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

DeleteAnyway, it's false.

I couldn't resist!

DeleteCan you give me an interesting counterexample?

Counterexample: 0^1 = 0^2 but 1 ≠ 2

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

DeleteCan anyone come up with a less trivial counterexample?

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

ReplyDeleteBeautiful!

ReplyDelete