>>12541604The only bs proofs are those that prove things that are obviously retarded. In this case, there is only one real example in modern mathematics: the existence of a non-measurable set. But the proof that started this nonsense is the proof that the real numbers can be well-ordered, a "fact" which is obviously false, and which required a long time to clarify, basically until Paul Cohen showed that you can make it false as easily as you make it true, so that it is more correctly false than true (that's not exactly correct, it took several years after Paul Cohen, but the main idea is Cohen's).
The proof that the real numbers can be well-ordered (put into an uncountable ordered list, so that each real number is at one and only one position, and the list has the property that it is discrete and finite when counting down, meaning that every subset has a least element) is as follows:
1. choose an element from every nonempty subset of R.
2. consider the entire set R, you chose an element (it's a nonempty subset of R), so call that the "first" element of R.
3. Now consider R excluding your first element. This is nonempty, so you chose something from it. Let this be the second element.
4. Now consider R exluding the first two elements. This is nonempty, so you chose an element from it. Let this be the third element.
This is an inductive procedure, so it extends to all integers, and then to all ordinals, which are linearly ordered collections which are inductive, like the integers. For the countable ordinals, this is not an intuitive paradox--- you can embed any countable ordinal in R. But when you admit uncountable ordinals, and R as a set, then you can show that there is an ordinal which exhausts R in this way.
