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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
The assumptions of a metric space except for symmetry.
Why is it important to start at the origin when you are graphing points?
It is important for beginners because the coordinates of the graphing points are measured from the origin. More expert users don't need to do so.
What absolute value inequality has 6 and -10 as two of its solutions?
There are many possible answers but the simplest is
|x + 2| = 8
Which point represents the origin?
On the Cartesian plane the x and y axes are perpendicular to each other and they meet at 90 degrees at the point of origin which have coordinates of (0, 0)
What is the equation of a line passing through -3 7 and having a slope of?
If the slope is m, then the equation is y - 7 = m*(x + 3)
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What is equation point slope form contains the points 8 10 and -4 2?
Points: (8, 10) and (-4, 2)
Slope: 2/3
Equation: 3y = 2x+14
How do you factor out 2x2 28x 980?
That depends on the - or + values of 28x and 980 which have not been given
What is the boolean expression for a 2 out of 3 OR gate?
If the inputs are ABC. The inputs required to give an output are ABC, AB, AC and BC. Using the Absorption law X + X.Y = X we can remove ABC, the inputs required are therefore AB, AC and BC.
How long is each side of the square if the area is 9 centimeters squared?
3 x 3 = 9cm2 So the length of each side of the square must be 3cm.
What is the first five powers of ten?
101 = 10 = ten
102 = 100 = hundred
103 = 1000 = thousand
104 = 10000 = ten thousand
105 = 100000 = hundred thousand
101 = 10 = ten
102 = 100 = hundred
103 = 1000 = thousand
104 = 10000 = ten thousand
105 = 100000 = hundred thousand
101 = 10 = ten
102 = 100 = hundred
103 = 1000 = thousand
104 = 10000 = ten thousand
105 = 100000 = hundred thousand
101 = 10 = ten
102 = 100 = hundred
103 = 1000 = thousand
104 = 10000 = ten thousand
105 = 100000 = hundred thousand
e is derived in several different ways.
One way is the infinite sum:
e = 1 + 1/1! + 1/2! + 1/3! + ...
Another is to note that the function 2^x has a gradient of approx 0.6931*2^x while 3^x has a gradient of 1.0986*3^x. Therefore by continuity (and the intermediate value theorem), there must be a value between 2 and 3 such that the gradient of the curve has the same value as the curve. This value is e.
Did you hear about answer on page 220 of pre algebra with pazzazz?
The answer is a question:
Did you hear about...
The famous rodeo rider who would do anything for a horse?
What is the difference between a postulate and theorem in Geometry?
A postulate is assumed to be true while a theorem is proven to be true. The truth of a theorem will be based on postulates.
How many gallons to fill up a truck with a V8 engine?
There is no direct relationship between the number of cylinders in an engine and the size of its fuel tank!
