A number with an infinite amount of decimal places cannot be defined.
On the contrary, it can easily be defined.
thus does not exist.
No numbers actually `exist' - they're all an abstraction, even the integers.
First off, by multiplying by ten, they lost one 9 at the end of the series.
Your objection assumes there is an end to the series. There isn't an end to the series, so your objection is moot.
The real question is: what do we mean by 0.999...? If it's a number with an infinite number of digits, then the arguments based on algebra are correct and 1=0.999...
I have my taskbar down one side of the screen, and when I want to work on something, I click on the thing I want to work on and work on it.
This is only an efficient way of doing this if each `thing I want to work on' maps onto a single application, or a single window.
What if you're working on a number of projects, each of which requires the use of a spreadsheet, a graphics program, a web browser, and some software for writing or presenting? If you assign each project to a separate virtual desktop then switching between these projects is a one-click operation. Without virtual desktops, you spend a lot of time hunting through windows.
Just read the essay. Makes me want to weep
I agree. The guy's a mathematician, and he wrote his essay in Microsoft Word!
Taking humans out of the loop can't overcome differences in the way vehicles handle.
On the contrary, that's exactly what a computer can do - and more reliably than a human (think of autopilots and fly-by-wire). The system would need to know the performance curve (especially braking performance) of each vehicle involved, but we understand physics pretty well and these things are easily quantifiable. If designed properly, the system would be constantly measuring and updating its model of the vehicle's performance in real time, and would take account of weather, road surface, etc.
Since when does ASLR improve performance or reliability?
To quote TFA: "If someone else is running your machine, it's more unreliable than if you're running it,"
growing the defense mechanism does not constitute an evolutionary disadvantage, so it stays in place.
Actually, the defense mechanism inevitably costs some energy to produce, and imposes design compromises that may affect the other functions of the plant. A mutant without these defenses will certainly have a fitness advantage.
However, while 1500 years sounds like a long time to us, it probably doesn't represent very many generations of these trees.
Open source licenses apply to the distribution of software. You are allowed to use GPL or other free software for any project that you use privately, with the proviso that any distributed version must be released under the GPL. If the software you wrote has some other restriction that prevents it from being released under the GPL, then it can't be distributed at all.
Your University holds the intellectual rights to the software you wrote, and therefore you can't release it under any license without their consent. This would apply whether the software contained GPL code or not. The GPL has clauses explaining these issues.
I have hardly ever known a mathematician who was capable of reasoning. -- Plato
