Cambridge Chat (previously New Cambridge Students Entry 2004)

It was mine too! I'm officially not a baby anymore and totally legal for drinking, clubbin....! But i can also go to jail now hehe the joy of being 18!

EDIT: hehe i just realised it is still my birthday in UK coz it's - 1H with France...

Hey guys - remember me from the mists of time past worrying last summer?

Hope you are all ok and not stressing about exams

i want to goto the library but I'm scared my bedder will come in here and killlll me for having the messiest room ever

OOO OOO OOO:

Can someone check my proof for the following:

Prove that the set of irrational numbers is uncountable...

For this I said take the set I as the set of irrationals. R = Q U I
i.e. that the real numbers is the union of the rationals and irrationals
But we know R is irrational and Q is rational, and so using the property that the union of countable sets is countable, I must be uncountable!

Is that right? Is there any other way to do it (which isnt horrendously complex mind you!)

so how would you do it as a proof by contradiction? Or the diagonal argument as well...I cant see how to use that (probably cos I dont understand it properly)!!??

so how would you do it as a proof by contradiction?

That's exactly what you just did, say so in your answer. Makesure you've also proved there isn't a bijection from N to R if you haven't used done that already in the question. I remember there being questions which made you go all the way back through to N rather than assuming the uncountablity of R.

A.

I suppose it depends on how many marks the question carry... you wouldn't prove R is uncountable for 2 marks would you? (having said that... you might have to if a quest explicitly asked for it...)

You guys have just destroyed any shred of doubt I had left about my decision not to do a maths degree.
I had a hunch it would be all about proof ...

this isnt in maths we're talking about...it's computer science!