can you please show me stepbystep how to do 4a and 4b 4 a Sh

can you please show me step-by-step how to do 4.a) and 4.b)?

4. (a) Show that the set of all finite sequences of the numbers 0, 1,… ,9 is countably (b) Show that the set of all infinite sequences of the numbers 0,1..,9 is uncountable. 5. (a) Suppose that each of n,is an odd integer, so that there exist integers infinite.

Solution

4a)

Actually the cartesian product of finite collection of countable sets are always countable

LetA={0,1,2,3,...9}

When infinite set is N{0,1,2,....,n}

Then A belongs to N

So it is countable in infinite

4b)

It is vice versa of the above

Let A={0,1,2,3,...9}

and N={0,1,2,...9)

When comparing it will be uncountable!