I'm not aware of any physical purpose either. I think the thing that makes this appealing is a mathematical fact that totally violates our intuitive concepts of numbers. We have to think on a higher level (which includes the concept of infinity) to make sense of the proof. The thing in the 1,000+ comments that surprised me is how many/.s don't understand the concept of infinity which says to me that they can't think on that higher level. Don't even think of talking about Fourier transforms with them!
I'm so glad I work with IBM iSeries servers where the hardware takes care of this and we don't need a DBA for this (every object is automatically spread among all disks in the storage pool).
IBM also has a utility that tells you how to match SSD with disk for the best overall performance. Then you only buy the SSD you need.
Lightstone's notation is just an artificial construction and I'm not sure what the value of it is. My problem with it is that, while appearing to embrace the concept of infinity, it violates the concept at the same time. This is like the part of mathematics where a proposition can be true and false at the same time. You are free to play in this world, of course, but I doubt that many/.s will follow you there. And certainly don't imply that LIghtstone's concepts are automatically valid because they aren't.
Sorry, I didn't realize that you had spelled it correctly the first time and just mistyped it the second. As you pointed out, I couldn't spell infintely correctly myself. The only number that's always lower than any number I come up with is negative infinity. My point is that the concept of an "infinitely low number" is included in the concept of infinity itself so we don't need to make that distinction.
Sink or swim: So, when you go over the bridge, you accept that the bridge is solid but you don't accept the result? So you jump in the water? 12 years from now, you'll still get grief for simultaneously accepting and rejecting the same concept.
The part you are challenging is "Let a =.999...". That isn't an assumption, it's an initial condition. The proof then proceeds to prove that "a" is also equal to one. Therefore, 1 =.999...
You're confusing the computer world with the mathematical world. In math, the square root of one has two solutions, +1 and -1. Square root is a short form of "Solve for x where x^2 -1 = 0." Because of the ^2, there are always two solutions, although one may be an imaginary number.
1/arbitrary low number = some high number. There, fixed that for you. There is no such thing as an "infinitly low number." In fact, "infintly" isn't even a word!
In my world, the floor function is only defined for numbers with a specific number of digits. Since my computer can't process the concept of infinity, I don't care what the floor function is of any number with an infinite number of digits.
Your logic is based on a finite number of digits, not an infinite number of digits. There is no such number as 0.000..01 (with the ".." representing an infinite number of digits. The concept of "infinite" is that you can never get to the point where you can put a 1 on the end.
There is no such number as 0.0000....01 (with the "...." representing an infinite number of digits. The concept of "infinite" is that you can never get to the point where you can put a 1 on the end.
In the United States, the protections for debit cards are similar to credit cards. According to Wikipedia, you may be liable for $500 of debits to a debit card if you wait more than two business days to report the unauthorized transaction. This only applies if you use it as a debit card (PIN entered); many people suggest using it like a credit card (signature required) for this reason. The other problem with debit cards that I'm aware of is getting overdraft charges and similar fees refunded by the bank if your debit card is misused.
Flukso is for Europeans. From the Web site: "from a current clamp attached to one of the two main power cables." (Emphasis added.) In the United States, you must use two current sensors, one for each main wire, for residential wiring. Obviously, three sensors are required for three-phase commercial power.
The "list of routers affected" at Notebooks.com is just a picture (.png) of a few rows of a spreadsheet. I would like the full list, please, even if just posted in a comment.
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I'm not aware of any physical purpose either. I think the thing that makes this appealing is a mathematical fact that totally violates our intuitive concepts of numbers. We have to think on a higher level (which includes the concept of infinity) to make sense of the proof. The thing in the 1,000+ comments that surprised me is how many /.s don't understand the concept of infinity which says to me that they can't think on that higher level. Don't even think of talking about Fourier transforms with them!
Okay, I'll bite: What's the difference between "a concrete idea" and "an abstract idea"? Your difference seems arbitrary at best.
Read some of the comments first and hopefully you'll understand.
I'm so glad I work with IBM iSeries servers where the hardware takes care of this and we don't need a DBA for this (every object is automatically spread among all disks in the storage pool).
IBM also has a utility that tells you how to match SSD with disk for the best overall performance. Then you only buy the SSD you need.
I thought were using successor to mean adding a 9 at the end. Now I don't know what you mean by successor.
Lightstone's notation is just an artificial construction and I'm not sure what the value of it is. My problem with it is that, while appearing to embrace the concept of infinity, it violates the concept at the same time. This is like the part of mathematics where a proposition can be true and false at the same time. You are free to play in this world, of course, but I doubt that many /.s will follow you there. And certainly don't imply that LIghtstone's concepts are automatically valid because they aren't.
I will concede that sqrt(x) means the principal square root if you will agree to always put the +/- in front of it.
Sorry, I didn't realize that you had spelled it correctly the first time and just mistyped it the second. As you pointed out, I couldn't spell infintely correctly myself.
The only number that's always lower than any number I come up with is negative infinity. My point is that the concept of an "infinitely low number" is included in the concept of infinity itself so we don't need to make that distinction.
If you look at it like this, .999... does have a successor: itself. If you add a 9 to the end, you have the same number you had before. Does that help?
Sink or swim: So, when you go over the bridge, you accept that the bridge is solid but you don't accept the result? So you jump in the water?
12 years from now, you'll still get grief for simultaneously accepting and rejecting the same concept.
Joe, Joe, take care of that bile duct!
The part you are challenging is "Let a = .999...". That isn't an assumption, it's an initial condition. The proof then proceeds to prove that "a" is also equal to one. Therefore, 1 = .999...
You're confusing the computer world with the mathematical world. In math, the square root of one has two solutions, +1 and -1. Square root is a short form of "Solve for x where x^2 -1 = 0." Because of the ^2, there are always two solutions, although one may be an imaginary number.
1/arbitrary low number = some high number. There, fixed that for you. There is no such thing as an "infinitly low number." In fact, "infintly" isn't even a word!
No, you can't add anything at the end, because you can't get to the end to add it. That's the concept of infinity.
Just because YOU don't understand it doesn't mean that it's flawed!
In my world, the floor function is only defined for numbers with a specific number of digits. Since my computer can't process the concept of infinity, I don't care what the floor function is of any number with an infinite number of digits.
Your logic is based on a finite number of digits, not an infinite number of digits. There is no such number as 0.000..01 (with the ".." representing an infinite number of digits. The concept of "infinite" is that you can never get to the point where you can put a 1 on the end.
There is no such number as 0.0000....01 (with the "...." representing an infinite number of digits. The concept of "infinite" is that you can never get to the point where you can put a 1 on the end.
Just because YOU don't understand the proof doesn't make it flawed. The proof is correct and has been for the 35+ years I've known about it.
In this case, putting the highest scores first puts the "crap, crap, crap" at the top. But it's a silly story to begin with, so who cares?
You said, "This move will lock up Minnesota's history for decades to come."
No it doesn't. All the new administration has to do is pass a law to void the contract. This is a government, not a business.
In the United States, the protections for debit cards are similar to credit cards. According to Wikipedia, you may be liable for $500 of debits to a debit card if you wait more than two business days to report the unauthorized transaction. This only applies if you use it as a debit card (PIN entered); many people suggest using it like a credit card (signature required) for this reason. The other problem with debit cards that I'm aware of is getting overdraft charges and similar fees refunded by the bank if your debit card is misused.
Flukso is for Europeans. From the Web site: "from a current clamp attached to one of the two main power cables." (Emphasis added.) In the United States, you must use two current sensors, one for each main wire, for residential wiring. Obviously, three sensors are required for three-phase commercial power.
The "list of routers affected" at Notebooks.com is just a picture (.png) of a few rows of a spreadsheet. I would like the full list, please, even if just posted in a comment.