- #1

Square1

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So how would one read the following for example...

set X = { u "member of" set A :|: u has property P}

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- Thread starter Square1
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In summary, :|: is a notation used in probability theory to indicate a condition or given set of elements to be considered in computing probabilities. It is pronounced as "such that" or "given" and adds a layer of complexity to the usual P(.) notation.

- #1

Square1

- 143

- 1

So how would one read the following for example...

set X = { u "member of" set A :|: u has property P}

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- #2

mathman

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- #3

SteveL27

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Square1 said:

So how would one read the following for example...

set X = { u "member of" set A :|: u has property P}

Have never seen that notation before. Assuming it has the same meaning as the more usual

set X = { u "member of" set A | u has property P}

I would pronounce that "such that."

- #4

Stephen Tashi

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Probabilities are assigned to subsets of some space of possible outcomes. If A and B are sets in such a space then [itex] A \cap B [/itex] and [itex] A | B [/itex] both refer to the set of elements in [itex] A \cap B [/itex], but the probability [itex] P(A | B) [/itex] tells us that probability is to be computed as if the elements of the "space of possible outcomes" are only those elements which are in B while [itex] P(A \cup B) [/itex] tells us that the "space of possible outcomes" is the original space of possible outcomes.

Hence the meaning of the notation P(X) is not as simple as "P(X) means the probability of the set (or event) X". When the "|" sign is used, the P(.) notation also tells something about what is to be considered the space of possible outcomes.

- #5

blue_raver22

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In probability theory, the symbol '|' is often used to represent the conditional probability of an event A given an event B, denoted as P(A|B). This means the probability of event A occurring, given that event B has already occurred.

In the context of set theory, the symbol '|' is used to represent the "such that" or "such that it satisfies" relation. In the given example, set X is defined as the set of all elements 'u' that are members of set A and also have the property P. This can be read as "set X is equal to the set of all elements 'u' such that 'u' is a member of set A and 'u' has property P."

The symbol ':' is used in set theory to represent the "such that" relation. In the given example, the use of two colons (:|:) can be read as "such that it satisfies." So, the overall meaning of the expression is "set X is equal to the set of all elements 'u' such that 'u' is a member of set A and 'u' has property P."

The symbol :|: is commonly referred to as the "vertical bar" or "pipe" symbol. It is used to denote a logical OR in computer programming, representing a choice between two options.

The origin of the symbol :|: can be traced back to the earliest days of computer programming and was likely inspired by mathematical notation. It has been used in various programming languages, such as C, Unix, and Perl.

In addition to representing a logical OR, the symbol :|: is also used in regular expressions to denote a character class, or a set of characters that can be matched in a string. It is also used in Unix command lines to separate commands that are executed sequentially.

Yes, there are a few other symbols that are similar to :|: in appearance and function. These include the double pipe symbol ||, which is used to represent a logical OR in some programming languages, and the single pipe symbol |, which is used to represent a bitwise OR.

While the symbol :|: is primarily used in computer programming, it has also been adopted in some online communication as a symbol for a hug or embrace. It can also be seen in various forms of art and design, but it is not commonly used in everyday language.

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