(no subject)

[prog]

Heh heh, pages upon pages of people going No... NO! Aaaaaagh you're all wrong shut up about the .999... thing. This is worse/more amusing than the time that the Monty Hall problem was AOTD.

I find it interesting that the text of the article actually predicts the belief-path the doubters take... when faced with simple and easily graspable proofs, they change their minds and state that obviously this means that the number system is broken.

Comments

[radtea.livejournal.com]

Even Godel's theorem wouldn't work if the rules of the system were inconsistent.

Which is why the response to Godel's theorem is ususally to say that mathematics is incomplete rather than inconsistent. What Godel showed is that any consistent axiomatic system that is rich enough to contain arithmetic contains true theorems that cannot be proven via deductive manipulations within the system. Such a system is said to be "incomplete".

To experimental scientists this was not exactly a big surprise, as we always viewed the kind of knowledge we created as more than just a hack to get at things that the theorists could get at by other means. The big surprise is that fifty years later pure mathematics has an even greater hold over theoretical physics than it did in Godel's day.

[chocorisu.livejournal.com]

Incomplete, certainly. But definitely not inconsistent.