دو خطا در SQL Server که الان به آن برخوردم و راه حل آن‏ها

تعریف عضو وارون

تعریف عضو وارون چپ و راست روشن است.

Definition. Let be a semigroup with identity e. Let a E S. If there exists an element b in S such that ab = e = ba,

then b is called the inverse of a, and a is said to be invertible.

Definition. A nonempty set G with a binary operation . on G is called a group jfthefollowing axioms hold:

(i) a(bc) = (ab)cfor all a,b,c E G. (ii) There exists e E G such that ea = afor all a E G. (iii) For every a E G there exists a' G such that a'a = e.

If the binary operation in a group (G,•) is commutative — that is. ab = ba for all a,b E G — then the group is called commutative or abelian.

تا اینجا: یک مجموعه که ضرب شرکت پذیر، عضو خنثی و وارون گروه. اگر ضرب جابجایی گروه آبلی

Let (S,') be a semigroup. Since- is associative, Theorem 4.2 (Chapter 1) holds here, and therefore there is a unique product of any given elements E S, in that order, that are written For any positive integer n we define, as before, a = aa...a (n-fold product), which is called the nih power of a. 

تعریف عضو خنثی

Definition. Let (S. ) be a semigroup. Ifthere is an element e inS such that ex—x=xe for aJixES,

then e is called the identity of the semigroup (S,).

تعریف right identity

 right identity مشابه left identity تعریف می‏ شود.

نکته

On 14th December 1900, German theoretical physicist Max Plank published his seminal paper on the Quantum Theory of Radiation, and quantum physics was born! In the early years of the 20th century, quantum physics was further developed and applied to explain several other experiments by Albert Einstein, Paul Dirac, Neils Bohr and many others.

Quantum theory is extremely non-intuitive, and came as a shock to the physics community, shaking the foundations of scientific knowledge. American physicist Richard Feynman once said, “I think I can safely say that nobody understands quantum mechanics.”

Though a century old now, its interpretations still puzzle scientists and students alike, making it a hot topic for research, with new ‘theories’ coming up all the time!

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SET versus SELECT when assigning variables?

SET is the ANSI standard for variable assignment, SELECT is not.

SET can only assign one variable at a time, SELECT can make multiple assignments at once.

If assigning from a query, SET can only assign a scalar value. If the query returns multiple values/rows then SET will raise an error. SELECT will assign one of the values to the variable and hide the fact that multiple values were returned (so you'd likely never know why something was going wrong elsewhere - have fun troubleshooting that one)

When assigning from a query if there is no value returned then SET will assign NULL, where SELECT will not make the assignment at all (so the variable will not be changed from its previous value)

As far as speed differences - there are no direct differences between SET and SELECT. However SELECT's ability to make multiple assignments in one shot does give it a slight speed advantage over SET.

تعریف left identity

Let (S, ) be a semigroup and let a,b E S. We usually write ab instead of a b. An element e in S is called a left identity if ea=a for all a E S.

مثال هایی از نیم گروه

Examples of semigroups are

(a) The systems of integers, reals, or complex numbers under usual multiplication (or addition) (b) The set of mappings from a nonempty set S into itself under composition of mappings (c) The set of n X n matrices over complex numbers under multiplication (or addition) of matrices

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نحوه نمایش یک ساختمان جبری

Any algebraic structure S with a binary operation + or is normally written (S,+) or (S,•). However, it is also customary to use an expression such as "the algebraic structure S under addition or multiplication." Examples of semigroups are

ساده ترین ساختمان جبری

The simplest algebraic structure to recognize is a semigroup, which is defined as a nonempty setS with an associative binary operation. 

ساختارهای جبری مهم

Algebraic structures whose binary operations satisfy particularly important properties are semigroups, groups, rings, fields, modules, and so on.