I've always thought of Pi as being infinitely precise
Sure, but so is any other number, assuming that by "infinitely precise" you mean that it occupies a single point on the real line.
between any pair of whole numbers, you can find an infinite number of rational and irrational values. So... which infinity is bigger? It would seem that the infinite set of whole numbers is eclipsed by the infinite set of irrational and rational numbers _between_ each pair of whole numbers
In fact, the set of all rational numbers is the same size as the set of all integers. This is because you can create a one-to-one correspondence between these two sets. The set of all irrational numbers, however, is larger than the set of all rational numbers. For more information, google "cantor's diagonalization."
You don't need to invoke a "special" frame of reference to have "instantaneous" time travel. Rather, it seems most natural to suppose that you would maintain your present zero-acceleration frame of reference.
So if I were on a world which was drifting through space at a constant velocity and not rotating, and I time-travel a day into the future, I shouldn't have any problems. If, on the other hand, I'm on a world which is accelerating (like the Earth), then time travel becomes unsafe.
Maybe there could be an irrational number whose infinite string happened to only contain digits 0 to 5?
Not "could be" - there definitely is such a number. For example, consider this number that I just made up:
0.50055000555000055550000055555000000555555.....
This is an irrational number; in fact I would bet that it is a transcendental number. Its decimal expansion never repeats, and yet it is easily predictable.
So what? Yes, curiosity is a survival mechanism - you are curious because, over millennia of evolutionary history, curious people produced more offspring on average than uncurious people.
This does not mean that curiosity itself is inextricably linked to a desire to survive, any more than the ability to walk is inextricably linked to a desire to survive. It's perfectly reasonable to expect to be able to build a walking robot, so what makes you think curiosity is any different?
No, because you're still limited by the amount of matter in the universe (And don't say that's just a technicality - it's exactly the same technicality that prevents a DFA from recognizing the language).
So should dictionaries also list words like rediculous, definately, and yuo? And should it's be listed as the possessive form of it? Should their, there, and they're all be interchangeable? That would reflect common usage, after all.
Certainly people understand what is meant by rediculous, so confusion is not an issue. But we already have a correct way to spell that word: ridiculous. Similarly, virus already has a plural: viruses. Virii doesn't even make sense, and a lot more people would be confused by virii than by viruses.
What you have described is called cardinal voting. The voter assigns each candidate a rating from some range. It can be 0 to 10, -1 to 1, or whatever. The ratings are totaled up and whoever has the most votes is elected.
In practice, this is the same as approval voting. Realize that it does not make sense to ever assign a zero. By assigning a -1 to candidates you don't approve of, you maximize the chance of electing the candidates you do approve of.
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Of course, the more general form, exp(x) = cos(x) + i sin(x), is much more useful.
I've always thought of Pi as being infinitely precise
Sure, but so is any other number, assuming that by "infinitely precise" you mean that it occupies a single point on the real line.
between any pair of whole numbers, you can find an infinite number of rational and irrational values. So... which infinity is bigger? It would seem that the infinite set of whole numbers is eclipsed by the infinite set of irrational and rational numbers _between_ each pair of whole numbers
In fact, the set of all rational numbers is the same size as the set of all integers. This is because you can create a one-to-one correspondence between these two sets. The set of all irrational numbers, however, is larger than the set of all rational numbers. For more information, google "cantor's diagonalization."
You don't need to invoke a "special" frame of reference to have "instantaneous" time travel. Rather, it seems most natural to suppose that you would maintain your present zero-acceleration frame of reference.
So if I were on a world which was drifting through space at a constant velocity and not rotating, and I time-travel a day into the future, I shouldn't have any problems. If, on the other hand, I'm on a world which is accelerating (like the Earth), then time travel becomes unsafe.
Eh? If one can be determined from the other, then it's a pretty reasonable assumption that they should be equally random.
So by your logic, 2.00000000... is just as random as 1.4142135623..., since each can be determined from the other?
The proof that PI is infinite is trivial.
The way you say this bothers me. Pi is not infinite; it is a real number between 3 and 4. It would make much more sense to say that Pi is irrational.
Maybe there could be an irrational number whose infinite string happened to only contain digits 0 to 5?
.
Not "could be" - there definitely is such a number. For example, consider this number that I just made up:
0.50055000555000055550000055555000000555555....
This is an irrational number; in fact I would bet that it is a transcendental number. Its decimal expansion never repeats, and yet it is easily predictable.
So what? Yes, curiosity is a survival mechanism - you are curious because, over millennia of evolutionary history, curious people produced more offspring on average than uncurious people.
This does not mean that curiosity itself is inextricably linked to a desire to survive, any more than the ability to walk is inextricably linked to a desire to survive. It's perfectly reasonable to expect to be able to build a walking robot, so what makes you think curiosity is any different?
That flowchart is broken. He never initialized counter.
Sorry, but this is one of my pet peeves. What's a beaurocrat? A member of a beauro?
a neutron star with the density of Sol would be roughly the size of a baseball
A neutron star with the density of Sol would not be a neutron star.
Hah, all those shopping carts that you have to plug will soon be obsolete.
No, because you're still limited by the amount of matter in the universe (And don't say that's just a technicality - it's exactly the same technicality that prevents a DFA from recognizing the language).
Nope. If it's 30 meters thick, yes, but if it's one centimeter thick, it will just burn up in the atmosphere.
So should dictionaries also list words like rediculous, definately, and yuo? And should it's be listed as the possessive form of it? Should their, there, and they're all be interchangeable? That would reflect common usage, after all.
Certainly people understand what is meant by rediculous, so confusion is not an issue. But we already have a correct way to spell that word: ridiculous. Similarly, virus already has a plural: viruses. Virii doesn't even make sense, and a lot more people would be confused by virii than by viruses.
Okay. 1+1=11 in unary.
And with overloaded operators, you can add two strings, so "1"+"1"="11".
Umm, no. You can accelerate at one gee forever and never reach light speed relative to your starting point.
Yeah, right. If that were true, McDonald's would go out of business.
That wouldn't explain how it came to be a moon of Saturn.
I think you mean that neandertals were smarter than their precursors.
As anybody who's seen a meter stick knows, a meter is more like 39 inches long.
Ariwhat? Play Go, you hippy!
What you have described is called cardinal voting. The voter assigns each candidate a rating from some range. It can be 0 to 10, -1 to 1, or whatever. The ratings are totaled up and whoever has the most votes is elected.
In practice, this is the same as approval voting. Realize that it does not make sense to ever assign a zero. By assigning a -1 to candidates you don't approve of, you maximize the chance of electing the candidates you do approve of.
If you meant "the slowest orbital speed of a non powered object (therefore the lowest true orbit) is"
No. The lower you are, the faster you have to go to orbit.
The parent was an excellent post. Congrats.
Well, of course gravity isn't linear. We already knew that.