You know, I should really learn to google things before I suggest "new" ideas ;)

They mentioned that the flow temperatures recorded in the hot pixels are colder than typical basaltic / rhyolitic flows and were speculating that they didn't catch freshly erupting material, but rather material that had a little time to cool. But I can't help but wonder.... does Venus have carbonatite flows? They're colder, and if there's anything Venus isn't short on, it's carbonic compounds...

(BTW, with those not familiar with carbonatite lava, its really weird stuff - incredibly fast-flowing and smooth (often less viscous than water), erupts looking black or dark gray like oil, doesn't (visibly) glow during the day (just a fast moving black substance), at night it has a weird maroon glow, and it oxidizes to bright white as it ages)

(Just one of many unusual types of volcano :) )

Ahh I think I see the problem, it was giving me the results for the city of Hyde near Manchester, not Hyde Park!

Okay, so according to the site, Dorking or Guildford to London is about an hour by rail during rush hour, 45 minutes during off-peak (15-20 quid each way); while according to Google Maps it's 1-2 hours during rush hour, 60-80 minutes during off-peak.

Except that there's nothing in the concept of infinity that is specific to sets, so cardinality is not really relevant unless we're specifically discussing infinite sets. Which we're not. We're discussing the limit of a single value that increases without bound as an input condition approaches a critical value. I'm sure you could rephrase that in terms of set theory, but that doesn't imply a fundamental dependence.

And frankly, if you've hung around Slashdot long you should realize that a rather large percentage of the community doesn't have a really firm grasp of much mathematics beyond basic arithmetic. That doesn't mean they're not interested in the concepts being discussed though, and nothing is gained by belittling either them or those who offer them simplified explanations.

When I was in the UK, I found a strong inverse correlation between "how close I was to London" and "how polite and friendly people were". I could only verify the rule out to Northern Ireland, but if it continues to hold up, then the people of the Pitcairn Islands have to be the friendliest people on Earth ;)

Victoria shows a much faster time - a bit over one hour and 15.70 quid. Probably because it has only one change (Hyde Park had three) and because I'm searching longer in advance. It's also possible that some routes were sold out at the last search time.

Still over an hour by rail, 1-2 hours by car, during rush hour (I'm searching for departure time 17:30 on a weekday each time - earlier it was today, now I'm searching for Monday)

Of course, the "rest stops" with their stockpiles of fuel and parts will probably be massive structures, so we'll also need "tug boats" to transfer the satellites from their original orbit to one that can dock with the rest stop, and then return it to it's designated orbit again after repair and refueling. Still far less energy-intensive than sending up a replacement satellite though. And if only refueling is needed then it's probably easier still to outfit the tug with a refueling waldo that can mate with a standardized fuel receptacle on the satellite - then the tug only has to make a single trip from the rest stop/fuel depo to whatever wonky orbit the satellite is in, and the satellite itself need never move at all.

It's not a number in the normal sense of the term, but using it as such is a simple and convenient shorthand for the far more complex and subtle mathematical concepts being expressed by the statement. In fact it's so radically simplified that even a layperson can kind of vaguely wrap their head around it, while you'll probably need a PhD in mathematics to really understand the underlying concepts.

You seem to be discussing asymptotes, which have a bit more subtle meaning. An asymptote is a line that a function gets infinitely close to without ever touching. Essentially the further you follow the asymptote the more it resembles the graphed function, but they will never be quite the same. 5/x gets two lines because it has two asymptotes: a horizontal asymptote at y=0, since the function gets infinitely close to y=0, but never actually reaches it no matter how large x gets, and a vertical asymptote at x=0 since the function gets infinitely close to x=0, but never actually reaches it no matter how large y gets.

Asymptotes don't themselves have anything to do with division by zero though - for example the well-behaved function x^2/(x^2+1) has a horizontal asymptote at y=1, since the function will get infinitely close to y=1 but never actually reach it, but it doesn't have a vertical asymptote since it's well-defined for all values of x.

Asymptotes don't even have to be aligned to an axis - for example, rather than a horizontal asymptote, the function y=x + 1/x gets a diagonal asymptote at y=x: the function will never quite touch that line, but the further you get from x=0 the closer the two resemble each other.

No, it's very context dependent. The usual way to deal with divide-by-zero and other discontinuities is to use the calculus limit operation, the "creeping up on it" I referred to. You can think of it as looking at a graph and, if the function behaves nicely except at that one point, taking the value that it looks like it should have if there weren't an infinitesimal gap present.

(lim x->0 ... is read as "the limit as x approaches zero of...")

lim x->0 1/x = does not exist (positive or negative infinity, depending on the direction you approach it from)
lim x->0 1/x^2 = +inf (the same from either side)
lim x->0 Ax/Bx = A/B
lim x->0 sin(1/x)/x = does not exist (oscillates smoothly between positive and negative infinity with an infinite frequency)

Ah, thought of one with a definite discontinuity: x/abs(x)
lim x->0+ x/abs(x) = 1
lim x->0- x/abs(x) = -1

Now absolute values may not get used a lot in normal calculations, but you may get the same effect if, for example, you're using square roots and only considering the positive result, as is extremely common in computations since standard data types can't hold an ambiguous value:
i.e. sqrt(x^2) = abs(x), rather than the mathematically correct +/-x

The biggest clue is that the large European manufacturer of airliners actually calls it an Airbus.

But if you don't need the allowance, Ryanair is still the best price by a country mile.

I keep thinking of converting a ski jacket so I can pack 2 weeks clothing in the lining (they never check the size of coats!) and go on a fortnight's vacation hand luggage only...

> What is wrong with presenting x/x as "1" at zero? When would that ever cause a problem in an application?

Probably nothing, assuming you've got a special case within your evaluation function that checks for encountering the discontinuity and returns the limit. That doesn't mean your function has a value at that point, only that you can fake it in a consistent manner that, in most applications, will result in a graceful workaround of what, in most contexts, is an annoying mathematical anomaly. But as I said such discontinuities can also be indicative of extreme behavior in the components - if this were a piece of engineering design software for example, hiding the discontinuity might conceivably result in a design with unsuspected vulnerablities.

Also, if you are getting such a well-behaved discontinuity, there's a good chance you could simply rearrange/simplify your equation so that the discontinuity is never encountered at all. E.g. algebraically x/x = 1, so why are you ever performing the division at all?

I hope it's also obvious that that is not something that can be gracefully generalized - without knowing the surrounding function there's no way to estimate what the limit at 0/0 might be (lim x->0 7x/3x = 7/3), or even if it has a limit at all.

No, you're right - you're a serf locked into a large city against your will. My mistake.