Hi everybody,
I need to prove the following sets are infinite sets by finding a countable in everyone of them:
a)
b)
c)
d)
How can I do this?
I was wondering if the following would be correct:
for example in (a): ,
where .
Thanks in advance for the help.
@jfk Just a correction to something you said:
Not every irrational number is transcendental. For example square roots of non-perfect squares are irrational, but not transcendental.
Hint for (c): functions from the naturals to {0,1} are essentially just countable sequences of 0's and 1's. Can you write down infinitely many such sequences? There are many ways to do this.
Hint for (d): elements of this set are essentially ordered pairs of natural numbers. Can you write down infinitely many such pairs?
10x DrSteve for the correction. Though I'm not sure I understood your example. I'm pretty confused about the relation (e.g: who contains who) between Irrational, Algebraic and Transcendental numbers, I would apreciate it very much if some one can help me make some order with those concepts.
is the set of all functions mapping .
Think characteristic functions
is the reverse of that.