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In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + is an elementary example of a geometric series that converges absolutely. There are many different expressions that can be shown to be equivalent to the problem, such as the form: 2 −1 + 2 −2 + 2 −3 +. Wrise® is an economical, multifunctional, microencapsulated leavening system for pizza and refrigerated/frozen dough systems. This product will not react until exposed to oven heat during the baking process. Typical usage is 1.0 - 3.0% of f.
IBM tape reel with white write ring in place, and an extra yellow ring.
From top to bottom: an unprotected Type I cassette, an unprotected Type II, an unprotected Type IV, and a protected Type IV.
A sheet of 51⁄4' floppy disk write protect tabs.
Write protection is any physical mechanism that prevents modification or erasure of valuable data on a device. Most commercial software, audio and video is sold pre-protected.
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Examples[edit]
- IBM 1⁄2 inch magnetic tape reels, introduced in the 1950s, had a circular groove on one side of the reel, into which a soft plastic ring had to be placed in order to write on the tape. (“No ring, no write.”)
- Audio cassettes and VHSvideocassettes have tabs on the top/rear edge that can be broken off (uncovered = protected).
- 8 and 51⁄4 inch floppies can have, respectively, write-protect and write-enable notches on the right side (8″: punched = protected; 51⁄4″: covered/notch not present = protected). A common practice with single-sided floppies was to punch a second notch on the opposite side of the disk to enable use of both sides of the media, creating a flippy disk, so called because one originally had to flip the disk over to use the other side.
- 31⁄2 inch floppy disks have a sliding tab in a window on the right side (open = protected).
- IomegaZip disks were write-protected using the IomegaWare software.
- Syquest EZ-drive (135 & 250MB) disks were write-protected using a small metal switch on the rear of the disk at the bottom.
- VHS-C, Video8, Hi8, and DVvideocassettes have a sliding tab on the rear edge.
- Iomegaditto tape cartridges had a small sliding tab on the top left hand corner on the front face of the cartridge.
- USB flash drives sometimes have a small switch, though this has become uncommon. An example of a USB flash drive that supported write protection via a switch is the Transcend JetFlash series.
- Secure Digital (SD) cards have a write-protect tab on the left side.
- Extensively, media that, by means of design, can't operate outside from this mode: CD-R, DVD-R, Vinyl records, etc.
These mechanisms are intended to prevent only accidental data loss or attacks by computer viruses. A determined user can easily circumvent them either by covering a notch with adhesive tape or by creating one with a punch as appropriate, or sometimes by physically altering the media transport to ignore the write-protect mechanism.
Write-protection is typically enforced by the hardware. In the case of computer devices, attempting to violate it will return an error to the operating system while some tape recorders physically lock the record button when a write-protected cassette is present.
Write blocking[edit]
Write blocking, a subset of write protection, is a technique used in computer forensics in order to maintain the integrity of data storage devices. By preventing all write operations to the device, e.g. a hard drive, it can be ensured that the device remains unaltered by data recovery methods.
Hardware write blocking was invented by Mark Menz and Steve Bress (US patent 6,813,682 and EU patent EP1,342,145)
Both hardware and software write-blocking methods are used; however, software blocking is generally not as reliable, due to human error.
References[edit]
- http://www.patentstorm.us/patents/6813682.html (US patent 6,813,682)
See also[edit]
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Write_protection&oldid=954026454'
Purplemath
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You never know when set notation is going to pop up. Usually, you'll see it when you learn about solving inequalities, because for some reason saying 'x < 3' isn't good enough, so instead they'll want you to phrase the answer as 'the solution set is { x | x is a real number and x < 3 }'. How this adds anything to the student's understanding, I don't know. But I digress..
A set, informally, is a collection of things. The 'things' in the set are called the 'elements', and are listed inside curly braces.
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For instance, if I were to list the elements of 'the set of things on my kid's bed when I wrote this lesson', the set would look like this:
{ pillow, rumpled bedspread, a stuffed animal, one very fat cat who's taking a nap }
Sets are usually named using capital letters. This isn't a rule as far as I know, but it does seem to be traditional. So let's name this set as 'A'. Then we have:
A = { pillow, rumpled bedspread, a stuffed animal, one very fat cat who's taking a nap } Ex libris 9 0 1 – a library database pdf.
The cat's name was 'Junior', so this set could also be written as:
A = { pillow, rumpled bedspread, a stuffed animal, Junior }
Sets are 'unordered', which means that the things in the set do not have to be listed in any particular order. The set above could just as easily be written as:
A = { Junior, pillow, rumpled bedspread, a stuffed animal }
We use a special character to say that something is an element of a set. It looks like an odd curvy capital E. For instance, to say that 'pillow is an element of the set A', we would write the following:
This is pronounced as 'pillow is an element of A'.
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The elements of a set can be listed out according to a rule, such as:
A mathematical example of a set whose elements are named according to a rule might be:
{x is a natural number, x < 10}
If you're going to be technical, you can use full 'set-builder notation' to express the above mathematical set. In set-builder notation, the previous set looks like this:
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The above is pronounced as 'the set of all x, such that x is an element of the natural numbers and x is less than 10'. The vertical bar is usually pronounced as 'such that', and it comes between the name of the variable you're using to stand for the elements and the rule that tells you what those elements actually are.
This same set, since the elements are few, can also be given by a listing of the elements, like this:
{ 1, 2, 3, 4, 5, 6, 7, 8, 9 }
Listing the elements explicitly like this, instead of using a rule, is often called 'using the roster method'.
Your text may or may not get technical regarding the names of the types of numbers. If it does, these are the symbols to use:
: the natural numbers
: the integers
: the rationals
: the real numbers
Yes, the symbols require those double-barred strokes for all the vertical portions of the characters.
Sets can be related to each other. If one set is 'inside' another set, it is called a 'subset'. Suppose A = { 1, 2, 3 } and B = { 1, 2, 3, 4, 5, 6 }. Then A is a subset of B, since everything in A is also in B. This relationship is written as:
That sideways-U thing is the subset symbol, and is pronounced 'is a subset of'.
To show something is not a subset, you draw a slash through the subset symbol, so the following:
..is pronounced as 'B is not a subset of A'.
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If two sets are being combined, this is called the 'union' of the sets, and is indicated by a large U-type character. If, instead of taking everything from the two sets, you're only taking what is common to the two, this is called the 'intersection' of the sets, and is indicated with an upside-down U-type character. So if C = { 1, 2, 3, 4, 5, 6 } and D = { 4, 5, 6, 7, 8, 9 }, then:
These are pronounced as 'C union D equals..' and 'C intersect D equals..', respectively.
Give a solution using the roster method:
A = { 1, 2, 3, 4, 5, 6, 7 }, B is a subset of A, the elements of B are even.
The set B is a subset of A, so it contains only things that are in A. The elements of B are even, so I need to pick out the elements of A which are even; these will be the elements of the subset B.
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The numbers in A that are even are 2, 4, and 6, so:
What is the intersection of A = { x is odd } and B = { x is between –4 and 6 }, where the elements of the two sets are integers?
Since 'intersection' means 'only things that are in both sets', the intersection will be all the numbers which are in each of the sets. The elements of B can be listed, being not too many integers:
The elements of A are all the odd integers. There are infinitely-many of them, so I won't bother with a listing. The intersection will be the set of integers which are both odd and also between –4 and 6. In other words:
Navicat premium essentials 12 1 1979. { –3, –1, 1, 3, 5 }
What is the union of A = { x is a natural number between 4 and 8 inclusive } and B = { x is a single-digit negative integer }?
Since 'union' means 'anything that is in either set', the union will be everything from A plus everything in B. Since A = { 4, 5, 6, 7, 8 } (because 'inclusive' means 'including the endpoints') and B = { –9, –8, –7, –6, –5, –4, –3, –2, –1 }, then their union is:
{ –9, –8, –7, –6, –5, –4, –3, –2, –1, 4, 5, 6, 7, 8 }
Give a solution using a rule: The set of all the odd integers.
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An odd integer is one more than an even integer, and every even integer is a multiple of 2. The formal way of writing 'is a multiple of 2' is to say that something is equal to two times some other integer; in other words, 'x = 2m', where 'm' is some integer. Then an odd integer, being one more than a multiple of 2, is x = 2m + 1.
So, in full formality, the set would be written as:
The solution to the example above is pronounced as 'all integers x such that x is equal to 2 times m plus 1, where m is an integer'.
It's a lot easier to describe the last set above using the roster method: Numi 3 18 3 download free.
{ .., –3, –1, 1, 3, 5, 7, .. }
Write 1 4 As A Decimal
The ellipsis (that is, the three periods in a row) means 'and so forth', and indicates that the pattern continues indefinitely in the given direction. Or, if the dots are between elements, like this:
..it means that the pattern continues in the same manner through the unwritten middle.
There's plenty more you can do with set notation, but the above is usually enough to get by in most algebra-class circumstances. If you need more, try doing a web search for 'set notation'.
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URL: https://www.purplemath.com/modules/setnotn.htm