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 June 7th, 2014, 01:30 PM #11 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 OK, but are there many interesting facts that require CH? Even if this is the case, CH then serves as as an axiom whose independence from other axioms and whose importance was realized in the 20th century. So we have AC and CH. Are there many more? I was saying that hunting for new axioms just to be able to justify interesting results is not a common occurrence. But even if it were, this does not change the concept of a formal proof (in the narrow sense). Or do you want to say that this concept of mathematics is deficient? For example, that we determine what's true intuitively rather than using formal derivations? Then how would you define a formal proof? June 7th, 2014, 01:49 PM   #12
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Quote:
 Originally Posted by Evgeny.Makarov OK, but are there many interesting facts that require CH? Even if this is the case, CH then serves as as an axiom whose independence from other axioms and whose importance was realized in the 20th century. So we have AC and CH. Are there many more? I was saying that hunting for new axioms just to be able to justify interesting results is not a common occurrence. But even if it were, this does not change the concept of a formal proof (in the narrow sense). Or do you want to say that this concept of mathematics is deficient? For example, that we determine what's true intuitively rather than using formal derivations? Then how would you define a formal proof?
The problem I have with CH as an axiom is that it's not obvious. It's not an obvious statement, which we clearly want for axioms to be. I place intuition above logic, yes. I just don't know enough about all this to answer. Maybe a formal proof is simply a way from one truth to another. Tags formal, proof Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post waqar-27 Applied Math 1 December 3rd, 2013 10:56 AM asifrahman1988 Calculus 1 March 17th, 2013 02:22 AM outsos Applied Math 0 July 29th, 2011 05:44 AM outsos Applied Math 3 May 27th, 2010 05:29 PM outsos Applied Math 2 May 26th, 2010 05:09 PM

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