Indeed. If you don't know where you're going, have your passenger navigate. If you don't have a passenger, pull the fuck over and read the map until you do know where you're going.
So, when someone was talking about taking his games (which are what he makes his living on) and handing them out for free, he reacted in a rational manner, and those people who were wanting something for nothing got their feelings hurt?
So if I buy a game of monopoly, which only comes with one set of instructions, and let my guests read those instructions, you think it's rational to threaten me with a lawsuit?
The fact that such numbers are infinitely scarce in an infinite set doesn't mean they don't exist. You're asserting that 1/infinity =0. I agree, but I'm more interested in the '1'.
If you really doubt that my number is in the set of all randomly generated numbers, try a gedanken where you generate all such numbers.
For one digit sequences, 9 of 10 fail to contain a 1. For 2 digit sequences 9 of 10 of the previous 9 fail to contain a 1. At 2 digits, we're already at 81 sequences. At the third position, 9 of 10 of that 81 fail to contain a 1. That's 729 sequences. Continue this process to infinity.
Surely you can see that we are generating these sequences fairly. Every digit has equal probability. You must also see that the number of sequences without a 1 increases monotonically. Therefore, even at infinity, there is a non-zero number of such sequences.
The scam these days focuses on uploaders. The fact that you purchased the disk doesn't grant you the legal right to distribute it. So if you're downloading your copy via torrents, you are still liable.
And I suppose the right wing French aren't clever enough to realize that if arab islamist websites can be censored, white christianist websites can be too.
Yes, but it is not a super set which is the issue. A subset can have additional properties that the super set doesn't have.
All I have to show is that there exists one member of the second set that does not contain every pattern. Since my number is in the first set, and the first set is a subset of the second set, then my number is in the second set. Since my number does not contain every possible pattern, it stands as a counter example to the original claim.
If knowledge of past digits doesn't help you predict what future digits will be, then it is random. All you can know about my sequence is that there is a 1 in 9 chance that the next digit will be any given digit. That's random.
Aspirin is not harmless either. About 10,000 Americans a year suffer gastric bleeding due to aspirin. There is absolutely a tradeoff to be made here. Don't go on aspirin therapy without fully considering the risks.
Secondly, just because the probability of a pattern appearing is one, that doesn't necessarily mean that the pattern will appear. For example, it's possible that the random sequence consists of only one digit.
Sorry, I misread this the first time. You're speaking of, e.g., an infinitely long sequence of 2s. If that's the case, the probability of any pattern containing any digit other than 2 is zero.
First of all, after removing the '1's, the digits in the resulting sequence aren't uniformly distributed
Sure they are. There's a 1 in 9 chance that the next digit will be 'n', for every digit except 1.
Secondly, just because the probability of a pattern appearing is one, that doesn't necessarily mean that the pattern will appear. For example, it's possible that the random sequence consists of only one digit
I did specify an infinitely long sequence.
Similarly, it's certainly possible that the infinite sequence doesn't contain any ones, but the probability of that happening is zero.
There are uncountably many irrational numbers. The chance of at least one of them having no '1' digits is 1. The chance of us picking that irrational number at random is 0.
When you drop all the 1's from the sequence, you are limiting in scope (for lack of a better term) the subset of possible sequences so that they no longer have 1 in them.
Yes, that's exactly what I'm doing. This proves that random sequences don't necessarily contain all finite sequences.
This doesn't prove the impossibility of containing every possible pattern when you similarly apply the same condition (ie, every pattern that doesn't contain a 1).
Why would you do that? The point is that there exists at least one infinite random sequence that does not contain at least one finite sequence. The fact that there are other finite sequences that are in the infinite random sequence is irrelevant.
Because Pi is irrational, my intuition tells me it would contain the encoding for every song.
My example proves your intuition wrong. It doesn't prove that pi fails to contain the encoding for every song. But it does prove that irrationality is not sufficient to support that claim.
Not every infinitely long random number contains every possible pattern. Consider an infinitely long sequence of digits. Now drop all '1's from the sequence. You still have an infinitely long series of random digits, in that knowing previous digits doesn't help you predict future digits. However, this infinite random sequence does not contain every possible pattern.
Whether this applies to pi or not, I have no idea.
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Indeed. If you don't know where you're going, have your passenger navigate. If you don't have a passenger, pull the fuck over and read the map until you do know where you're going.
Indeed. I can get $2 CRT monitors at my local Goodwill that will do 1600x1200 easy, and usually higher.
An armed tournament is a polite tournament.
So, when someone was talking about taking his games (which are what he makes his living on) and handing them out for free, he reacted in a rational manner, and those people who were wanting something for nothing got their feelings hurt?
So if I buy a game of monopoly, which only comes with one set of instructions, and let my guests read those instructions, you think it's rational to threaten me with a lawsuit?
At infinity, it would be 0.
The fact that such numbers are infinitely scarce in an infinite set doesn't mean they don't exist. You're asserting that 1/infinity =0. I agree, but I'm more interested in the '1'.
If you really doubt that my number is in the set of all randomly generated numbers, try a gedanken where you generate all such numbers.
For one digit sequences, 9 of 10 fail to contain a 1. For 2 digit sequences 9 of 10 of the previous 9 fail to contain a 1. At 2 digits, we're already at 81 sequences. At the third position, 9 of 10 of that 81 fail to contain a 1. That's 729 sequences. Continue this process to infinity.
Surely you can see that we are generating these sequences fairly. Every digit has equal probability. You must also see that the number of sequences without a 1 increases monotonically. Therefore, even at infinity, there is a non-zero number of such sequences.
I have cooked both wild caught and farm raised salmon. They both remain pink.
The scam these days focuses on uploaders. The fact that you purchased the disk doesn't grant you the legal right to distribute it. So if you're downloading your copy via torrents, you are still liable.
Yes, exactly.
And I suppose the right wing French aren't clever enough to realize that if arab islamist websites can be censored, white christianist websites can be too.
It is certainly true that some people Simply Aren't Interested in ye olde western enlightenment values
This is looking less and less like "some", and more and more like "most".
Yes, but it is not a super set which is the issue. A subset can have additional properties that the super set doesn't have.
All I have to show is that there exists one member of the second set that does not contain every pattern. Since my number is in the first set, and the first set is a subset of the second set, then my number is in the second set. Since my number does not contain every possible pattern, it stands as a counter example to the original claim.
That's not funny, it's true. Since "due process" no longer means "judicial process" what's left?
The resulting sequence is random by the set {0,2-9} but not by the set {0,9}.
The first set is a subset of the second set.
If knowledge of past digits doesn't help you predict what future digits will be, then it is random. All you can know about my sequence is that there is a 1 in 9 chance that the next digit will be any given digit. That's random.
Aspirin is not harmless either. About 10,000 Americans a year suffer gastric bleeding due to aspirin. There is absolutely a tradeoff to be made here. Don't go on aspirin therapy without fully considering the risks.
Secondly, just because the probability of a pattern appearing is one, that doesn't necessarily mean that the pattern will appear. For example, it's possible that the random sequence consists of only one digit.
Sorry, I misread this the first time. You're speaking of, e.g., an infinitely long sequence of 2s. If that's the case, the probability of any pattern containing any digit other than 2 is zero.
First of all, after removing the '1's, the digits in the resulting sequence aren't uniformly distributed
Sure they are. There's a 1 in 9 chance that the next digit will be 'n', for every digit except 1.
Secondly, just because the probability of a pattern appearing is one, that doesn't necessarily mean that the pattern will appear. For example, it's possible that the random sequence consists of only one digit
I did specify an infinitely long sequence.
Similarly, it's certainly possible that the infinite sequence doesn't contain any ones, but the probability of that happening is zero.
There are uncountably many irrational numbers. The chance of at least one of them having no '1' digits is 1. The chance of us picking that irrational number at random is 0.
When you drop all the 1's from the sequence, you are limiting in scope (for lack of a better term) the subset of possible sequences so that they no longer have 1 in them.
Yes, that's exactly what I'm doing. This proves that random sequences don't necessarily contain all finite sequences.
This doesn't prove the impossibility of containing every possible pattern when you similarly apply the same condition (ie, every pattern that doesn't contain a 1).
Why would you do that? The point is that there exists at least one infinite random sequence that does not contain at least one finite sequence. The fact that there are other finite sequences that are in the infinite random sequence is irrelevant.
Because Pi is irrational, my intuition tells me it would contain the encoding for every song.
My example proves your intuition wrong. It doesn't prove that pi fails to contain the encoding for every song. But it does prove that irrationality is not sufficient to support that claim.
Not every infinitely long random number contains every possible pattern. Consider an infinitely long sequence of digits. Now drop all '1's from the sequence. You still have an infinitely long series of random digits, in that knowing previous digits doesn't help you predict future digits. However, this infinite random sequence does not contain every possible pattern.
Whether this applies to pi or not, I have no idea.
It's not hactivists that are a threat to the net. It's the corporations and government agencies that the hactivists target that are the real threat.
If you haven't watched Torchwood yet, I'd advise against it. It's really pretty bad.
He ages, but incredibly slowly. On one episode of Torchwood, he spends nearly 2000 years buried underground and emerges no worse for wear.
Yes. As someone who drinks from the Ogallala Aquifer daily, fuck yes, I'm concerned.
What bothers me is wondering what sort of changes in the weather can be expected during the rest of the year after such an unusually warm winter
Forget the weather. Watch out for bugs this summer!
You can't get that KDE skin almost anywhere.