Yes.

Regards,

J.P.

We are doing the complex numbers questions for the project. For the 2012 Project Maths paper( question three) if we draw a geometric sketch for part (a) does this count as having answered part(b) which asks for a sketch on the argand diagram?

]]>What about part (ii)

Regards,

J.P.

I am doing the complex numbers question for the homework and I am not sure whether im answering the questions the way you want.

For 2010, question 3 b, I started by subtracting from to find and using this with the formula i was able to find a value for . I showed and the argument of on a graph.

I was just wondering is this enough information for the answers you are looking.

Click to access LC003ALP100EV.pdf

Thanks for your help.

]]>For (a) (i) you must prove the statement for ALL points in any finite set and functions on that finite set. So no, you can’t pick a distinguished point, set or function.

You must do this abstractly by starting with: let be an element of a finite set and …

The idea is that because the ‘universe’ (of states) is so small (finite), complicated behaviour can not occur.

The corresponding statement for not-finite or infinite sets is the following:

“Suppose that is a not-necessarily finite set and . Then all of the points of ” are eventually periodic.

However this is NOT correct. Two counterexamples:

1. In the dynamical system given by the doubling mapping, the point that we constructed with a dense orbit,

is NOT eventually periodic.

2. In the dynamical system given by the squaring function on the complex numbers, . We might see on Wednesday that the point

is NOT eventually periodic when — i.e. when is irrational.

The statement is correct when is finite.

Regards,

J.P.

In relation to the project, number one of the projects, for the first part must we formulate our function?

I understand how to get an eventually periodic point from a infinite set but how do i get one from a finite set?

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