Suppose you believe that to be the case, and then you observe such a coin landing on edge? In other words, what do you do when certain knowledge encounters an absurd event (unity prior vs impossible evidence)? There is no recovery from that, any more than you can say that infinity minus infinity is 5. The numbers one and zero do not behave like probabilities. In order to conclude that an even has certainty 1, you must observe infinitely strong evidence about it. Even in a math journal, a carefully reviewed published paper does not come close to infinite evidence.

Really? I don't think 100% certainty means what you think it does. Have you ever made a mistake proving a theorem? Has a peer-reviewed published theorem ever later been found to have a mistake? Is it even remotely possible that it will happen in the future? If so, you need to assign a level of certainty to any given theorem: a probability that it has a mistake. As it gets used more a scrutinized more, that probability declines dramatically, but it can't reach zero. Zero and one are not probabilities. There's a big difference between 0.99999999, or any other finite number of nines, and infinite nines. For the same reasons that infinity is not a real number, zero and one are not probabilities or certainties.

It's really hard to get a job without an Internet connection. Sure, it can be done, but it's harder. It's almost as important as having a phone number and address. Would it be cheaper to subsidize Internet access than to pay unemployment benefits? Or to forgo the taxes that get collected from people who are employed?

No, I'm talking about both. Having IPv6 on the internal network, with public IPv6 addresses (properly firewalled, of course), makes VPN easier.

That's what firewalls are for. The fact that NAT and firewall often go together in IPv4 does not mean it has to be that way. Just set your IPv6 firewall to deny by default, and you'll have the same security setup you usually get with NAT+firewall on IPv4, but with more flexibility.

Most people can set up IPv6 networking at home with a tunnel broker or similar. You can probably get it working on your laptop when traveling, provided the firewalls aren't too brain dead. So having your business support it will make it easier a lot of the time, but not all the time.

IPv6 makes VPN a lot easier and more reliable. Many small businesses care about that so that their employees can work while at home or traveling.

The decay to a non-zero constant one doesn't have tight conditions: f(n)=a*f(n-1)+c will decay to a constant for -1<a<1. In higher order equations the behavior is similar.

Second- or higher-degree difference equations can also oscillate stably, decay to a non-zero constant, or decay to a linear function.

You are part of the reason that software sucks so badly.

"The software has errors" is still "the software has errors", even if some errors make their presence felt less frequently.

On a related note, I'm curious what part of this is a "mistake". I think a better headline would be something like "SFPD Breathalyzer Fraud Puts Hundreds of DUI Convictions In Doubt".

Patents exist solely to promote innovation. Or, more specifically, "science and the useful arts". There is plenty of evidence that traditional industrial patents do exactly that. There is very little evidence that software patents do so, and plenty of evidence that they stifle innovation.

This isn't about morals. It's about asking what bargain society wants to make with innovators, in order to promote innovation. The software patent bargain is helping neither society at large nor innovators. Making sure that the lawyers like it is not one of the goals here.