h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

This is a rather curious problem I have run into. I have a feeling its solution will involve cauchy's limits but cannot be certain. I would be interested if this problem has been postulated or solved before. I would also like to know if it is easier in the hyperreals.

The problem is posted at http://www.h2g2.com/A376751 for your enjoyment. I may have made a trivial mistake in which case I apologise now.

For those wanting a brief intro to the article, what happens if you decide on a spurious rounding system where you round up or down from different points, not just the one halfway between the level of accuracy. I am trying to generalise a way to represent this and find some uses for it.

Any help will be useful. Thanks.

I read it, but my head exploded. Sorry.

Hmm... It seems I get most of my mathematical inspiration while sitting in the bath. The answer just comes to me and I can see a problem or solution.

I am stuck too... don't worry about it

I'm sorry every one, I have an affection for lost conversations like this one. I just had an irresistable urge to add something to the last entry. Sorry if I confuse anyone with this. Maybe the original writers could say something? Well I'll leave this newly reborn conversation to find its way back to the end again.

Thanks,
Mr Terran

Oooh... forgotten about this one.

Its worrying that I've been on the Guide so long...

I wouldn't worry about it. I guess in another two years some one will take one of my conversations from the bottom of the pile. Oh well...

Nice Talking to you,
Terran

The required condition implies a + d = a, therefore d=0, therefore c/g=0.

Therefore gamma must be infinite. Any cardinality of infinity will work fine, so I'd go for plain old boring aleph nought.

The best idea, though, is to redefine d to be cg and not c/g, thus allowing the following:

g=0: always rounds up
g=0.5: traditional rounding
g=1: always rounds down

Yep, I agree with 26199, though its not necessary to get into cardinalities to talk about what you need g to be such that c/g = 0. It's valid to talk about using an 'extended real number line', which has an extra element added to just the reals, called infinity (I like to write it as 'oo'), with extra rules like oo + x = oo for x any real, or x/0 = oo for x any nonzero real etc. Then it all works, though the cg rather than c/g works without needing to introduce more stuff.

*likes nice elegant solutions*

*wishes he could edit the entry and considers whining at Abi to give him a new password to the account*

*decides to go and read more stuff on functional programming for now*



Thanks for that 26199 though

Hey Henry