# IA Numbers and Sets Course Page (now updated to 2004).

#### Note added 19th October 2004. The following message does not
seem to have fully registered with everybody: if you are trying to do
questions on the first examples sheet then it may help to look at
"Comments on Examples Sheets" below, where some of the basic definitions
we haven't yet got to in the course are given. You don't need to know
all that much to tackle the questions.

### Examples sheets.

Sheets 1 to 4 are available in .dvi and .pdf format.

Here I have written a small amount about a couple of questions that
might cause confusion for one reason or another. (In particular, if
you are supervised after only a week of the course, then there will
be definitions that you have not yet come across. This page provides
some of them.)

### Further reading on this website.

Here is a pdf file of the first draft (rough in places and I shall
certainly make changes) of an article from a
book I am editing and partly writing. You may find it useful
preliminary/supplementary reading for the part of the course that
deals with functions, relations, binary operations and so on.

The language and grammar of mathematics.

The following of my mathematical
discussions are particularly suitable for those just starting
a degree course in mathematics.

A dialogue concerning the
existence of the square root of two.

What is wrong with thinking of
real numbers as infinite decimals?

A dialogue concerning the need for the
real number system.

Why is multiplication commutative?

What is naive about naive set theory?

Paradoxes concerning definability.

How to discover a proof of the fundamental
theorem of arithmetic.

How to discover the statement and two proofs
of Fermat's little theorem.

The definition of `definition'.

Is the phrase `well-defined'
well-defined?

What is `solved' when one solves an
equation?

The implication of implication.

Not perhaps directly relevant to the course, but in a very
roundabout way it might help train you to cope with questions
like Number 12 on Sheet 4.

This is here to help when we come to Examples Sheet 4. I hope it
will be enough to enable you to tackle at least some of the questions
on countability on the sheet. Countability is covered right at the end
of the course - hence the need for this page.