Recent content by ashnicholls

The proofs were stated above, I didnt want to list the whole thing, i just wanted to check that what i had written made sence. ok cheers. but the rest makes sence?

Cheers, Is what I have written here correct? "With these proofs he could then go onto show that any real number that is not in the set of algebraic numbers is a transendental number. And he also showed that because the set of real numbers is far larger than the set of integers, and...

Yes ok sorry, I was just being lazy. What is the proof that you can't count the set of real numbers?

Oh there is one more thing why did people critise this method?

ok thanks for your help, I will run with that thought now. Hopefully that is all I need.

Right, I thought I had it but I have lost lost it now. Am i right in thinking that he said if a set is countable, then it does not contain transendental numbers. So as the set of real numbers is not countable it contains transendental numbers, Is that the logic behind it?? If so how did...

And I have found some where in my notes that: The of Cardinality of A, the set of algebraic numbers, is aleph null, which is correct, A is countable, algebraic numbers are not transendental but it then says on the same line, so there are many transcendentals, how can you come to that...

No I understand countable, ie The sets has a 1-1 correspondence with N. But don't really get what you mean: Countable pertains to sets, not real numbers. The SET of algebraic numbers is countable. The set of real numbers is uncountable. Thus the set of algebraic numbers is 'almost none' of...

sorry that has gone straight over my head, group/set theory is not a strength of mine. Cheers

yes sorry I know he didnt prove there existence, he just made a method to show other number were transcendental. eerrrrrrrrrrrrrrrrrrr of course, all real are uncountable, so most are transcendental, obvious, thanks. Any more info you can give? How do all of you know all of this...

Does he mean though, if a number is not countable, its non algebraic so its transcendental? Is that the gist of it? Cheers

Yes sorry I should have said I undestand that, but how does he go on to say most numbers are transcendental, only a few are surely??

Does anyone know how Cantor showed the existence of Transcendental numbers. How can he say that most numbers are transcendental? Is that why everyone critised it? Cheers Ash

Yes that what I know already but don't understand, How do I relate it to my question? Cheers

I am sure I did a search and that never came up, cheers will have a look.