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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
How is the convergence of a sequence defined?
Let B, D be a metric space, p be any positive number, m be a positive integer, and {sn}, n Є N be a sequence in B. Then sn converges to a point c Є B if given there's an m for every p such that n > m, then sn Є N(c, p), the D-pneighborhood of c. c is said to be the limit of sn and can be written sn --> c.
See related links for more information.
How many second does days have?
While certain famous equations, such as Albert Einstein's E = mc^2, hog most of the public glory, many less familiar formulas have their champions among scientists. LiveScience asked physicists, astronomers and mathematicians for their favorite equations; here's what we found:"It is still amazing to me that one such mathematical equation can describe what space-time is all about," said Space Telescope Science Institute astrophysicist Mario Livio, who nominated the equation as his favorite. "All of Einstein's true genius is embodied in this equation." [Einstein Quiz: Test Your Knowledge of the Genius]
"The right-hand side of this equation describes the energy contents of our universe (including the 'dark energy' that propels the current cosmic acceleration)," Livio explained. "The left-hand side describes the geometry of space-time. The equality reflects the fact that in Einstein's general relativity, mass and energy determine the geometry, and concomitantly the curvature, which is a manifestation of what we call gravity." [6 Weird Facts About Gravity]
"It's a very elegant equation," said Kyle Cranmer, a physicist at New York University, adding that the equation reveals the relationship between space-time and matter and energy. "This equation tells you how they are related - how the presence of the sun warps space-time so that the Earth moves around it in orbit, etc. It also tells you how the universe evolved since the Big Bang and predicts that there should be black holes."
How do you do the equation 4dividedby3 pi radius cubed Example please?
It's used in finding the volume of a sphere which is: Volume = 4/3*pi*radius3
What is the value of Remington 1100 serial m124188v?
DEPENDING ON THE CONDITION,THEY GO AROUND 300TO 500 DOLLAR RANGE.IF YOU GO TO THE REMINGTON SITE THEY WILL TELL YOU MORE INFO...
How to prove that differentiating in the space of smooth functions is a linear transformation?
Recall that a linear transformation T:U-->V is one such that
1) T(x+y)=T(x)+T(y) for any x,y in U
2) T(cx)=cT(x) for x in U and c in R
All you need to do is show that differentiation has these two properties, where the domain is C^(infinity). We shall consider smooth functions from R to R for simplicity, but the argument is analogous for functions from R^n to R^m. Let D by the differential operator.
D[(f+g)(x)] = [d/dx](f+g)(x) = lim(h-->0)[(f+g)(x+h)-(f+g)(x)]/h
= lim(h-->0)[f(x+h)+g(x+g)-f(x)-g(x)]/h
(since (f+g)(x) is taken to mean f(x)+g(x))
=lim(h-->0)[f(x+h)-f(x)]/h + lim(h-->0)[g(x+h) - g(x)]/h
since the sum of limits is the limit of the sums
=[d/dx]f(x) + [d/dx]g(x) = D[f(x)] + D[g(x)].
As for ths second criterion, D[(cf)(x)]=lim(h-->0)[(cf)(x+h)-(cf)(x)]/h
=lim(h-->0)[c[f(x+h)]-c[f(x)]]/h
since (cf)(x) is taken to mean c[f(x)]
=c[lim(h-->0)[f(x+h)-f(x)]/h] = c[d/dx]f(x) = cD[f(x)].
since constants can be factored out of limits.
Therefore the two criteria hold, and if you wished to prove this for the general case, you would simply apply the same procedure to the Jacobian matrices corresponding to Df.
What are the effects of co relation on linear transformation?
Correlation has no effect on linear transformations.
What is the definition of an abelian group?
An abelian group is a group in which ab = ba for all members a and b of the group.
What is the value of a model 94 purchased in 1992 and is 99 condition?
Impossible to answer until you tell us WHO made it, WHAT caliber it is
The domain is all the first coordinates in a relation. A relation is two ordered pairs.
What is the rule for the sequence 3.7 3.2 2.7 2.2?
The difference between successive terms is 0.5.
You could write this as tn+1 = tn - 0.5 and t0 = 3.7
or tn = 3.7 - n/0.5, for n = 0, 1, 2, ...
What is 2 over 3 times 2 over 3?
4/9. Get yourself 9 pennies. Now divide those into 3 equal parts. Remove one of those parts [1/3] and mix the remaining pennies [2/3] up. Now take those pennies and divide it into 3 equal parts. Remove one part [1/3 of those pennies]. You now have 4 pennies out of the original (9 pennies.) What is the rule that you could have used to come up with the answer without using pennies?
Play around with 12 pennies and do some fraction multiplications. See why there are so many old measuring systems based on the number 12 and not 10.
When would you require a number be to the fourth power?
Using Stefan's law to find the emittance of a bodies radiation in Watts.
F( force in Watts--unit time per unit surface) = (a constant called the Stefan-Boltzmann constant )* T4 (temperature in Kelvin )
Algebra is a mathematical function in which using variables and numbers to solve a solution for a variable.
E.g. 1x+2y=3x
x=4
1(4)+2y=3(4)
4+2y=12
2y=8
y=4
to help us learn more in maths and learn differant methords
What is the value of model 94 serial number 2487282?
You have to tell us who made it, provide a detailed description of all markings and tell us the finish and overall condition if you want a good answer. Otherwise it could be 50-5000 USD or more.
There are many uses of algebra. Algebra is used mosty to find the value of the variable in a mathematic situation. Example- 3x=66 (divide by 3x on both sides)= 66/ by 3 is 22 solution- x=22 ----
