PIN fraud

That's almost begging the question. What I don't follow is what it is about irrationals that makes them impossible to enumerate in this way.

Try it, there isn't any way to make a list of (say) integers with a list of irrationals next to them with a one to one correspondence.

Not good enough. It may not seem like it to you, but I'm really a mere fallible mortal. Just because I might fail if I try, doesn't mean it can't be done, it might just mean I'm not up to the job.

I'd like to see a proof that it is impossible.

The strength of rot-13 can be doubled by applying the method twice :)

Yes, and in so far as there are bound to be an infinite - even if only countably infinite - number of ways of attempting a one-to-one it's barking up the wrong tree. There was a similar problem surrounding fermat's last theorem - you could have gone on forever failing to find an a,b,c such that a^n+b^nc^n but it wouldn't rule out the possibility that one fine day...

sorry that should have been "=" not ""

-lemma 5

"Jim" wrote

Nice link, thanks.

It's amazing how you recollect the proof after reading just the first bit of it!

Edivue (view?)

Produced for editing magnetic tapes. I only ever came across 1 bottle and that was 30 years ago. Its was intended for editing a cough or similar out of an audio tape. Quite a messy performance.

Alternatively, with a professional tape deck with access to the tape head you could simply mark the start/end of the cough with a chinagraph pencil and chop it out with a (non - magnetic!) razor blade or scissors.

You could see it but I'm not sure it would possible for the resultant image to be decoded manually, it depends on the encoding method. FM, M^2 FM, NRZ, something else? Data bits mixed with clock bits! And that's if Edivue still did the business at the high density of information on a magstripe.

DG

Me too.

Isn't it just. :-(

Nearly 40 years ago for me and I wasn't really paying attention then - more enjoyable this time.

Absolutely. This story made me smile. Chip and PIN has been going for some time down under, but calling itself eftpos.

I wonder how they will solve the problem at service stations here. If a PIN pad lasts a couple of months before it gets smashed in New Zealand, the same pad wouldn't last a couple of days here.

"Timothy Lee" wrote

... or even, *any* number! ;-)

Eg: function1 is (10 x T) as T approaches infinity, function2 is (5 x T) as T approaches infinity. Now, function1/function2 is *always* exactly 2 (two) - hence the limit is also 2. Not one or infinity!

Now there's an idea - I'll take it in the other direction (infinitessimal) and call it calculus.

"Jim" wrote

I think that's been done before! [By two different famous people, long ago...]