In article <firstname.lastname@example.org>, email@example.com wrote: > I think I should mention that there's also a question of trueness. > > Granted, there's the issue of whether or not a given person can prove > this or that statement, but there's also the question of truth. > > Are those statements true, or not?
Since you are doing a proof by contradiction and you are assuming at the start that you have integers x, y, and z that are solutions of the Fermat equation, then even false statements will be true (under your assumptions).
We could make a distinction between "derivable" and "true". Thus, we could say that all of your statements in your proof of FLT might be derivable, some of which are true, and others false.
This gets back to what several people have requested that you do. If a statement is true independent of the Fermat counterexample, then you should separate out such statements as lemmas or propositions. This would make analysis of your proof easier.
> But, hey, if they're true (ignoring the question of whether or not > I've proven them for the moment) then a simple proof of Fermat's > Last Theorem quickly follows.
This does not follow at all. There are many true statements in mathematics that do not have simple proofs.
> However, you have seen people arguing for months that I haven't > proven those statements, and the insinuation is that the > statements are false.
There is no insinuation that your statements are false. In fact, David Libert has already proved they are true by invoking Wiles theorem.
> I doubt that many of you would believe that such simple math isn't > provably true or not; therefore, I submit that it is reasonable to > conclude that these people are claiming the statements are false.
It might be reasonable to you, but we are not claiming the statements are false. We are claiming that you have not derived them.