Recent content by L²Cc

But does your example fit the relation? Don't the variables have to be integers? Going by your definition, if I do find a few cases that fit the relation and a few that don't, does that still mean the relation is an equivalence relation? Therefore, if let's say all variables are the same, ie...

Homework Statement Let X be Z*Z, i.e. X is the set of all ordered pairs of the form (x; y) with (x, y) are integers. De fine the relation R on X as follows: (x1^2, x2^2)R(y1^2, y2^2) = (x1^2 + x2^2) = (y1^2 + y2^2) Homework Equations By definition, an equivalence relation bears the...

So you're suggesting that the largest order for S_8 is 8? But can it be 15? Referring back to my example...

Homework Statement http: What is the largest number which is the order of an element of S_8? Write down an element of that order in disjoint cycle notation. Homework Equations The Attempt at a Solution To start with, I don't understand the wording of the question. When it refers...

Makes sense. Thank you!

oh right right! in other words, f(1) = 1 f(2) = 2 f(3) = 2 functions f(2) and f(3) would have been injections had a and b in the following f(a) = f(b)were equal which is not the case here? Surjections have have the property that for every y in the codomain there is an x in the domain such...

Homework Statement List all the functions from {1,2,3} to {1,2} representing each function as an arrow diagram. Which of these functions are (a) injective, (b) surjective, (c) bijective? For each surjective function write down a right inverse. Homework Equations The Attempt at a...

hmm I see, I never did that before, I simply went on with the integrating whenever it was 1/2-1/2cos2t for example...and I always obtained the right answer, weird! But thank you!

So you're suggesting that the integral of 1/2cos(2t) is 1/2sin(2t) ?! (can you please elaborate as to how you came up with the answer?)

Following your reasoning, 1/2*sin(2t) becomes 2x*sqrt(1-x²). The two cancels out when I plug it back into 1/2*sin(2t), and this can't be since the answer is 1/2*x*sqrt(1-x²)??!

Oh I see, you used the trig identity...and then I refer back to the triangle to figure out what's cos(t)...Thank you!

Homework Statement After integrating x²/(sqrt1-x²) using the triangle method and thereby substituting sin¤ for x, I ended up with the result 1/2¤-1/2sin2¤+c. For my answer toge complete, I must have the ¤ in x format. I managed to convert the 1/2¤, which is simply 1/2arcsinx but I couldn't...

Homework Statement After integrating x²/(sqrt1-x²) using the triangle method and thereby substituting sin¤ for x, I ended up with the result 1/2¤-1/2sin2¤+c. For my answer toge complete, I must have the ¤ in x format. I managed to convert the 1/2¤, which is simply 1/2arcsinx but I couldn't...

Using a graphical app, I measured the slope at every point and none equal the average rate??! Thank you.

Homework Statement In the previous question, we're asked to determine the average flow rate from 00:00 on 28 October to 00:00 on 2 November, which I did by finding the slope connecting these two points. The slope is -1/6 and so the average rate is -1/6 cfs/hours. The question that follows...