The inequality operators generally work on real numbers, not discrete numbers, and thus you say “nine is less than ten” just as you would say “nine pounds of flour is less than ten pounds of flour”.
For discrete, countable quantities, however, you still use “fewer”.
E.g. you would say that nine database records is fewer than ten records (we’re comparing countable quantities) because nine is less than ten (now we’re comparing real numbers in general).
It’s a sort of debit card which requires you to fill out paperwork every time you pay someone and they won’t know whether or not you actually had the money in your account until several days later.
Still... you are suggesting that I multiply 6-digit numbers in my head. Or multiply one by itself, anyway. By the time I get to the end of the multiplication I’ll have forgotten the beginning of it.
Perhaps you meant manually, not mentally... i.e. on paper, without a calculator.
And then you want to drive 90 MPH while tailgating someone because your car is so damn safe that you’d walk away from a head-on collision with a brick wall.
Not anything; only thermodynamically infeasible things.
Without adding power from some other source, you cannot split water and then use it for energy. It costs more energy to split the water than you can get back from the hydrogen when you burn it. Your combustion engine is limited by the Carnot cycle.
If you have power from some other source, you’d waste some of it if you used it to split water to get hydrogen. Although it is still conceivable that the net efficiency of using the available energy to split water and harvesting the hydrogen for fuel would be more efficient than your means of using the available energy directly.
What I was trying to say by a “consistent” transformation system is that any cube which is solvable from A must also be solvable from X.
To borrow another person’s analogy, though:
If you took a cube in state B, put new stickers on top of the old ones so that it was solved S, then there would be some state X, reachable in 20 moves or less, at which point you could peel off all the topmost stickers and the cube would be left in state A.
At this point, you could apply the same solution in reverse to go from A to B directly in 20 moves or less.
there are also a fair number of studies which show that birth order DOES make a difference in the personality of children. I think there is plenty of room to wonder whether the lessening (parental) anxiety you describe...does have a significant impact
It could also have just as much to do with having older siblings.
He wasn’t talking about rotating the entire cube, he was talking about rotating a single face 180 degrees.
Normally I think of 3 primary moves for each face: F, F', and F2 for instance, corresponding to a 90 degree clockwise turn, a 90 degree counterclockwise turn, and a 180 degree turn.
What he is claiming is that F2 shouldn’t count because it’s equivalent to either FF or F'F'. However, since F' is equivalent to FFF, should that not count either? As I see it, rotating one face through any degree turn is one move, whether that is 90, 180, or 270 (-90) degrees.
Note that the arrangement is not fully arbitrary: there are some arrangements which it is impossible to reach. Not only of the stickers, either (everyone knew that you could make a cube unsolvable by moving the stickers around, right?): it is possible without moving any of the stickers to arrange the pieces themselves in such a way that it is impossible to reach the solved state without taking the cube apart again.
However, among reachable arrangements, your statement is valid. I suspect you probably knew that, but other people mightn’t have.
To answer that question, you need to ask whether there is something inherently special about the “solved” state.
Or, to put it differently:
1) Begin in state A 2) Re-arrange stickers into a corresponding state X, such that state A maps directly to state X in a particular transformation system 3) Solve from state X to S (max. 20 moves) 4) Re-arrange stickers using the same transformation system in reverse, obtaining state B, which mapped to state S in that transformation system
Now, if your transformation system was consistent, you should be able to omit steps 2 and 4, going straight from A to B in 20 moves.
Slashdot Mirror
Not to mention ours, theirs, yours, mine, and whose...
All possessive pronouns are spelled without an apostrophe.
His, hers, and its are all possessive pronouns. None of them have an apostrophe.
It’s is the contraction of “it is”.
Ah ha! I knew something smelled fishy.
In mathematics, is the < operator referred to as 'fewer than" if it is operating on the set of integers?
I wasn’t aware that the relational operators could take sets as arguments.
The inequality operators generally work on real numbers, not discrete numbers, and thus you say “nine is less than ten” just as you would say “nine pounds of flour is less than ten pounds of flour”.
For discrete, countable quantities, however, you still use “fewer”.
E.g. you would say that nine database records is fewer than ten records (we’re comparing countable quantities) because nine is less than ten (now we’re comparing real numbers in general).
It’s a sort of debit card which requires you to fill out paperwork every time you pay someone and they won’t know whether or not you actually had the money in your account until several days later.
When facebook tells me that I havent contacted a dead person in a long time and I should try to re-connect with them, it is slightly upsetting.
I adblocked that div with an element hiding rule. I don’t need it suggesting when I should reconnect with my friends in the first place.
You can multiply 6-digit numbers in your head with no problem?
Frankly I’m sure that I could do that too if I spent forever practicing. However, it isn’t worth my time.
Still... you are suggesting that I multiply 6-digit numbers in my head. Or multiply one by itself, anyway. By the time I get to the end of the multiplication I’ll have forgotten the beginning of it.
Perhaps you meant manually, not mentally... i.e. on paper, without a calculator.
Or the ABS kicked in way earlier than it should have, which is more typically what I notice when driving vehicles with ABS.
And then you want to drive 90 MPH while tailgating someone because your car is so damn safe that you’d walk away from a head-on collision with a brick wall.
You can write with pencil or pen? That'd be - if you're normal and writing in Latin script, with your left-hand, and moving from left to right.
No... I’m normal and writing in Latin script, with my right hand, from left to right. I only write left-handed when I’m particularly bored.
salt, pepper, garlic and nutmeg
One of those spices does not belong with the others.
Although, it does go quite nicely with cinnamon, allspice, and cloves.
Not anything; only thermodynamically infeasible things.
Without adding power from some other source, you cannot split water and then use it for energy. It costs more energy to split the water than you can get back from the hydrogen when you burn it. Your combustion engine is limited by the Carnot cycle.
If you have power from some other source, you’d waste some of it if you used it to split water to get hydrogen. Although it is still conceivable that the net efficiency of using the available energy to split water and harvesting the hydrogen for fuel would be more efficient than your means of using the available energy directly.
First grade (called Grade 1 in some metric system nations) is a year of primary education in schools in the United States of America and English-speaking provinces of Canada. It is the first school year after kindergarten. Students are usually 6 to 7 years old.
If you don’t know what you’re talking about, please to be shutting the hell up.
I thought you “have no idea” what she meant. So I told you. If you really had no idea, now you know. And if you already knew, you’re an asshat.
Either way, her quote was wrong of course. I’m not defending that.
It takes more energy to split hydrogen and oxygen apart than can be recovered by putting them back together again.
6 years old at the beginning of the first grade, possibly 7 years old by the end of it.
What I was trying to say by a “consistent” transformation system is that any cube which is solvable from A must also be solvable from X.
To borrow another person’s analogy, though:
If you took a cube in state B, put new stickers on top of the old ones so that it was solved S, then there would be some state X, reachable in 20 moves or less, at which point you could peel off all the topmost stickers and the cube would be left in state A.
At this point, you could apply the same solution in reverse to go from A to B directly in 20 moves or less.
there are also a fair number of studies which show that birth order DOES make a difference in the personality of children. I think there is plenty of room to wonder whether the lessening (parental) anxiety you describe...does have a significant impact
It could also have just as much to do with having older siblings.
He wasn’t talking about rotating the entire cube, he was talking about rotating a single face 180 degrees.
Normally I think of 3 primary moves for each face: F, F', and F2 for instance, corresponding to a 90 degree clockwise turn, a 90 degree counterclockwise turn, and a 180 degree turn.
What he is claiming is that F2 shouldn’t count because it’s equivalent to either FF or F'F'. However, since F' is equivalent to FFF, should that not count either? As I see it, rotating one face through any degree turn is one move, whether that is 90, 180, or 270 (-90) degrees.
Note that the arrangement is not fully arbitrary: there are some arrangements which it is impossible to reach. Not only of the stickers, either (everyone knew that you could make a cube unsolvable by moving the stickers around, right?): it is possible without moving any of the stickers to arrange the pieces themselves in such a way that it is impossible to reach the solved state without taking the cube apart again.
However, among reachable arrangements, your statement is valid. I suspect you probably knew that, but other people mightn’t have.
I never said it wasn’t easy. What isn’t easy is doing a “mirror symmetric problem” with no practice.
Saying the alphabet backward is easy too, but that’s because I practiced it.
zyxwvutsrqponmlkjihgfedcba
To answer that question, you need to ask whether there is something inherently special about the “solved” state.
Or, to put it differently:
1) Begin in state A
2) Re-arrange stickers into a corresponding state X, such that state A maps directly to state X in a particular transformation system
3) Solve from state X to S (max. 20 moves)
4) Re-arrange stickers using the same transformation system in reverse, obtaining state B, which mapped to state S in that transformation system
Now, if your transformation system was consistent, you should be able to omit steps 2 and 4, going straight from A to B in 20 moves.
QED.
1) Turn the lights off.
The cube now exists in an entangled solved/unsolved state.