Recent content by aleph-aleph

Wow... Thanks everyone! That's very informative for me. I'll look for those threads. =)

This might sounds stupid but I'm just curious, what is the best programming language we have today?

Thanks pi.

Hi all, I got a BSc in Mathematical Science (not very good result: 3.00/4.00) but I'm interested to further my study in Logic and Foundation of Mathematics. Can I take MSc in Logic and Foundation of Mathematics with such result? If can, which university you guys would recommend?

I agree that there is nothing contradictory in Halmos (1960), just my random thought that there might be a misinterpretation since Cantor himself didn't bothered by the paradoxes and his original papers are difficult to read and understand. Check these out...

Naive set theory is defined using daily language because the mathematics at that time has not been formalised yet. Naive set theory has a lot of ambiguity because of the impreciseness of language. Perhaps some misinterpretation occur when mathematicians axiomatised set theory.

Cantor's diagonalisation argument is not the only proof. He gave his first uncountability proof in his 1874 paper "on a property of the set of real algebraic numbers".

I'm doing Bachelor Degree in Mathematics and have difficulties in study because every time I study I tend to ask "what" and "why" instead of "how". As a result, I often trap myself into the metaphysics and philosophical part of mathematics and unable to proceed further. I tried to ignore it but...

Cantor didn't define "first element" nor mention "least element" but I think I get what you guys are saying. This is what I get, there is no concept of "relation" to Cantor, for Cantor, "well ordered" kinda means "can be listed in such a way that it has first element". For example set of even...

Include the null set.

I'm reading Cantor's 1883 Grundlagen, it says a set is well-ordered if the set and it's subsets have first element, the next successor (unless it's an empty set or there is no successor). Note that the first element not neccessarily a least element. "Theory of sets" by E. Kamke also give the...

If you mean theorem that produce larger cardinality, it's the power set P(n)=2^n where n is cardinal number. http://mathworld.wolfram.com/PowerSet.html

Does anyone know where to get the letters(English translation) between Cantor and Dedekind during the development of set theory??

I think if we going to discuss about the topic, we better do it in mathematical way. Apart from that, you can watch the videos about M theory for more information. http://www.youtube.com/watch?v=J4Hn7l7jDY8&list=PL029DEA05B111AA1D

The negation of the statement should be x≤xt => x>1 instead of x≤xt ∧ x>1. Other than that, I believe your proof is valid.