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Abstract Algebra

Have you ever wondered what would happen if you redefined some of the basic rules of algebra so that concepts you took for granted, like AB = BA, no longer apply? Abstract algebra does just that through the study of the properties that define algebraic structures. Post all questions about fields, rings, group theory, vector spaces, and the axioms that define them into this category.

1,849 Questions

What is the value of a model 1892 25-20?

The Blue Book of Gun Values, which can be confusing (daunting?), and The Standard Catalog of Firearms, or Flayderman's Guide to Antique American Firearms, are good places to start (often appearing at a library near you). First, as you'll find, the weapon needs to be "graded" (See NRA Condition Grading Definitions... (http://www.oldguns.net/ ) Remember that these are only "guides" to help determine assumed worth of a weapon; real "value" (price, actually) is determined by the amount someone is willing to pay for the piece and your acceptance of their offer. If you are serious more than curious, take it to a "real" (certified) appraiser (or at least two to get, like, a Dr's "2nd opinion" because "your mileage may vary").

What are the implication if there is no algebra?

I want to answer this question at a deeper level and a shallow level. At a shallow level it is very easy to answer. All that is required is to list the applications of mathematics and to put a big cross over it. Algebra is as fundamental to the whole field of mathematics as letters, words and grammar are fundamental to language and literature. So, at a shallow level, your question is really asking what the applications of mathematics in society are.

In a civilised society nearly everything has required mathematics at one point. Things like computers, washing machines and radios (basically everything that requires electricity) all require mathematics. Things like chairs, carpet, glass, concrete, and plastic (basically everything manufactured and/or built) all require mathematics. Things like cars, boats, trains and airplanes (basically all vehicles) all exist because of mathematics. Mathematics has other more continuous applications in society that are not "objects" such as the transport system, the economy, the medical system, immigration and communications. These are only a fraction of the applications of mathematics. Essentially you could not have a civilised society without mathematics.

Now I want to answer this question at a deeper level. Algebra is a natural consequence of a normal human thought process. Because of this the only way algebra wouldn't exist is if we were just like the monkeys in the trees. Algebra essentially represents our intelligence as humans.

Algebra represents a thought process called deductive reasoning. Deductive reasoning (or deduction) is a process where you find a definite consequence of a known fact or facts. Let me show you an example. Say there are two kids and a broken vase. They both accuse the other of breaking the vase. We know for a fact that both these kids are making contradictory statements (contradictory meaning cannot be true at the same time). Because of this fact we also know that at least one kid must be lying. So here our known fact is that the kids contradict each other and our definite consequence is that at least one must be lying (it's also possible that both are lying, something else may have broken the vase). In algebra our known fact might be that three plus an unknown number equals six (3+x=6). We also know that because these equal each other we can subtract three from both (3-3+x=6-3). So therefore our definite consequence is that our unknown number equals three (x=3).

My point is that if we didn't have algebra then we wouldn't have deductive reasoning. Deductive reasoning is very similar to another thought process called inductive reasoning. Inductive reasoning is a process where you find a PROBABLE consequence of a known fact or facts. Let's look at an example. You know that every time you go to your friend's house they have white walls. They have not told you that they are going to paint the walls so you assume that next time you go to their house their walls will still be white. This is probably going to be true but it's still possible that something will happen and the walls won't be white.

We are constantly using inductive and deductive reasoning all the time. 99% of the time we don't think about it. Because algebra (and the rest of mathematics) is a natural consequence of our normal thought processes its absence would only be possible if humankind was much more animal like. That's why I say the only way algebra wouldn't exist is if we were just like the moneys in the trees.

What is the value of a Remington 700 ADL rifle?

I recently came across the 700 ADL at Wal-Mart. It was a 30-06 and they were asking $518.00.

What are identities in algebra?

An equation in which the variable(s) can take any value and it is still true.

ex.

cos(x) = cos(-x)

sin(x) = -sin(-x)

The above equations are true for any real value of x. Identities are sometimes written with a "triple equals sign", as in 3 parallel lines rather than 2.

What is the value of an 1896 penny?

It is 1 penny.

If you want to know its value in another currency you will need to specify which country the coin comes from (many countries use a penny) and in what currency you want it to be valued.

What is a quaternion?

, in mathematics, are a non-commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. They find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations, such as in 3D computer graphics. Since the affine transformations representable by matrices are a superset of quaternion rotations, matrices are employed as a computationally suboptimal but geometrically equivalent orientation representation in many calculations. Vectors cannot represent rotations per se, only directions, and so are generally unsuitable unless the calculation in question assumes a fixed "up" direction.

In modern language, quaternions form a 4-dimensional normed division algebra over the real numbers. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by (Unicode ℍ). It can also be given by the Clifford algebra classifications Cℓ0,2(R) = Cℓ03,0(R). The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only three finite-dimensional division rings containing the real numbers as a subring.Graphical representation of quaternion units product as 90°-rotation in 4D-space, ij = k, ji = −k, ij = −ji

Why is magnetic field vector a pseudo vector?

It is the cross product of two vectors. The cross product of two vectors is always a pseudo-vector. This is related to the fact that A x B is not the same as B x A: in the case of the cross product, A x B = - (B x A).

What is the difference between the functions rand random srand and randomize?

RAND: Rand uses a multiplicative congruential random number generator with period232 to return successive pseudo-random numbers in the range 0 to RAND_MAX.

Return Value: Rand returns the generated pseudo-random number. RANDOM(): Random returns a random number between 0 and (num-1).random(num) is a macro defined in STDLIB.H.

RANDOMIZE(): Randomize initializes the random number generator with a random value. Because randomize is implemented as a macro that calls the time function prototyped in TIME.H, you should include TIME.H when you use this routine

SRAND(): The random number generator is reinitialized by calling srand with an argument value of 1.The generator can be set to a new starting point by calling srand with a given seed number.

What is the difference between a conjecture postulate theorem and corollary?

Conjecture: a statement which may or may not be true.

Postulate: a statement that is believed to be true, but may not be.

Theorem: a statement that has been proved to be true provided some postulates are true.

Corollary: a statement whose truth follows from the truth of a theorem, but one which is not important enough to call it a theorem.

How did algebra get started?

Algebra, as the Arabic origin of its name suggests, originated with the work of the Persian mathematician al-KhwÄrizmÄ« (780 – 850).

What is college algebra?

College Algebra is the required math for all college students.

What is the value of a Colt 1908 380 circa 1911?

I ppayed $400 for mine in 70 percent condition. Have seen them as high as $800 in like condition. For value ask: felix@bedians.com

How many seconds are there in 3 days?

Calculated Time

There are 259,200 seconds (4320 minutes) in 3 days.

Riddle answer

If this is a trick question, then there is only one "second" in three days. The first day, the SECOND day, and the third.
259,200 seconds.

What is the value of a 1972s penny?

Unless it's a proof coin, 1¢

Note that this site has a Coins and Currency thread for asking questions about, well, coins and currency. Money and Credit is for things like checks, credit cards, loans, etc.

What is the value of a 1991 pfennig?

One-half of a U.S. cent.

Before the euro was adopted Germany's currency unit was the mark. One mark = 100 pfennige (that's the plural of "pfennig"). At its last valuation in 2002 the mark was worth about 50 cents (U.S.) so a pfennig was pretty far down on the scale.

What is the factored form of 8x3 27 equals 0?

Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals".

8x3 + 27 = 0 => (2x + 3)*(4x2 - 6x + 9) = 0

What is the advantage of using completing the square vs the quadratic formula?

Completing the square is advantageous in several situations:

  • usually, it requires fewer steps than the quadratic formula, reducing the potential for error.
  • it allows you to determine the exact value of the answer instead of a decimal approximation.
  • it allows you to determine imaginary solutions.

What is The sum of 3 times a number and 7 is 19?

If: 3x+7 = 19

Then: 3x = 19-7

And: 3x = 12

So: x = 12/3 = 4