Rudin reperesents Bourbaki-style maths, i.e. it is packed with generality. It is NOT an introductory text. I advise you to work with Zorich, "Mathematical Analysis" instead. It has a gentle introduction to abstract concepts and makes things clearer and visual by using examples from physics and...
Rudin reperesents Bourbaki-style maths, i.e. it is packed with generality. It is NOT an introductory text. I advise you to work with Zorich, "Mathematical Analysis" instead. It has a gentle introduction to abstract concepts and makes things clearer and visual by using examples from physics and...
Hey, Guys!
I wonder what applications of Ramsey's famous theorem there exist apart from such cases as:
1) constructions of functions in the domain of natural numbers to check some properties of sequences of real numbers.
2) propositions about points in convex postition (Erdos-Szekeres...
OK, NateTG thought in terms of an injection into a set, while I thought about a bijection onto a subset of a given set.
So the empty map is always an injection, right.
Nimz, if I'm not mistaken from the quotation follows that the strict inequality in NateTG's post is justified too!
What...
So is the empty map useless, obscure?
But how can we speak about cardinality and countability then??
OK, Guys I seem to need more info on this matter. Give me some links or references, please! :rolleyes:
The US has enough money but it's in the wrong hands, like in any other country. But it's not the country that matters most. It's the problem of the whole World! WE're off the track, Guys!
As I said the problem is difficult. SETI must obey the "jungle law" - the strongest survives. But it's a...
Hm, why injection?? You meant bijection, didn't you? You need it to show "not larger", so we biject a set X onto a subset Z of Y to show that cardX<=cardY (since cardX=cardZ)
Nevertheless I think I got it. I forgot about the empty map.
So we can map the empty set onto a subset of any set X...
"So if somebody wants to find us let'm do it" - sounds pretty egoistic and fully indifferent, don't you find??
I think a civilization which doesn't make just a bit of effort to search for anybody of its own kind simply does not deserve to be called "advanced"!
Why? Because so it has already...
The empty set is finite, so it must be countable!
But which bijective mapping do we actually have here??
Does it depend on whether we take 0 as a natural number or not?
I've never thought of it before...
I don't understand why it should be bad if people spend most of their time doing mathematics. I think everyone is devoted to some sort of activity in his/her life. It's obsession in its purely positive sense. It's love, which gives their life the grounding purpose. And I'm sure it'll hardly be...