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1. ### Is the group of permutations on the set {123} Cyclic? Justification required

Homework Statement Consider the group of permutation on the set {123}. Is this group cyclic? Justify your answer Homework Equations The Attempt at a Solution I wrote out the cayley table for this group, and noticed that if we take (123)^3 = e . Seeing as we can get back to the...
2. ### Squeeze Theorem - Multivarible question

Hi, I'm having a lot of difficulty with finding limits of multivariable functions. A question like this comes up every year in the final exam and it will always ask for use of the squeezing theorem. Homework Statement (a) Suppose that f(x, y) = 1 +(5x2y3)/x2 + y2 for (x, y) =/=...
3. ### Group Theory (Abstract algebra manipulations)

Homework Statement Let a,b,c,d be elements of a group G and let ab = c, bc = d, cd = a, da = b. Examine the expression da^2b and first derive an expression for b in powers of a. Then express c and d in powers of a. Show that a^5 = e (identity element) Homework Equations The Attempt...
4. ### Resits exams in the summer.

Hi, By leaving everything to the last minute I managed to flunk all my math courses this year. As such I now have 4 resit exams in August to prepare for. The courses are Introduction to Analysis Sets and Algebraic structures Linear Algebra Advanced Calc (goes up to about Calc II level...
5. ### Second Order Partial Derivatives + Chain Rule

Homework Statement Let z = z (x,y) be a function with x = x(s), y = y(t) satisfying the partial differential equation (Ill write ddz/ddt for the partial derivative of z wrt t and dz/dt for the total derivative of z wrt t, as I have no idea how to use Latex.) ddz/ddt +...
6. ### Convergent Sequences problem

Homework Statement Let f: N -> N be a bijective map. for n Є N a sub n = 1 / f(n) Show that the sequence (a sub n) converges to zero. Homework Equations The Attempt at a Solution Basically I have been stuck on this problem for hours now and have read through my notes and...
7. ### Equivalence relations and classes problem.

Homework Statement Let X = {a,b,c,d}. How many different equivalence relations are there on X? What subset of XxX corresponds to the relation whose equivalence classes are {a,c},{b,d} Homework Equations N/A The Attempt at a Solution So I wrote out all the possible "blocks"...