Homework Statement
How many elements of order 4 are in S6? (symmetric group with order 6)
Homework Equations
The Attempt at a Solution
So, the different forms of elements with order 4 in S6 are
(abcd)(ef), (abcd)
from there I am sunk on how to calculate. I know there are...
Homework Statement
Hello,
I have some data from a statewide standardized exam, and I am trying to do a regression model, but am having a bit of trouble. (Im a mathematician and not a statistician).
Basically, I am trying to show some type of correlation between race and test scores...
Homework Statement
1)Show, if E is a subset of D is a subset of the real numbers R and f maps D into R is uniformly continuous, then the restriction of f to E is also uniformly continuous.
2)Show, if f is continuous and real valued on [a,b) and if the limit of f(x) as x approaches b...
Homework Statement
suppose f: [a,b] ---> Q is continuous on [a,b]. prove that f is constant on [a,b].
Homework Equations
The Attempt at a Solution
Since there is at least one irrational number between every two rational numbers,
then for f to be continuous in the given scenario...
Homework Statement
part 1)Show the function a(x)=|x| is a continuous function from R to R;
part 2)
Prove that if the functions f: D--> R is continuous at x=a, then l f l (absolute value of f) is also continuous at x=a.
Homework Equations
The Attempt at a Solution
part 1)...
Homework Statement
function f is differentiable when x=0,
f'(0) is not equal to zero for all real Numbers
f(a+b) = f(a)f(b)
show f'(x) = f'(0)f(x)Homework Equations
The Attempt at a Solution
f(x+0) = f(x) = f(x)f(0)
this shows f(0) = 1
then i get stuck..
Homework Statement
function f is differential when x=0,
f'(0) is not equal to zero for all a,b(real Numbers)
f(a+b) = f(a)f(b)
show f'(x) = f'(x)f(x)
Homework Equations
The Attempt at a Solution
f(a+b) = f(a)f(b) for all a,b(real numbers)
f(0), a+b=0
then f(0) =...
Homework Statement
for function f:[a,b]--> Q is continuous on [a,b],
prove that f is constant on [a,b]
Homework Equations
The Attempt at a Solution
proof by contradiction,
suppose there is a k, such that a<k<b,
since f is continuous on [a,b], there must be a j...