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Loser66
 one year ago
I don't understand the socalled "Axiomatic method." I need a super patient helper to help me out.
Please, explain me.
Loser66
 one year ago
I don't understand the socalled "Axiomatic method." I need a super patient helper to help me out. Please, explain me.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What, in particular, do you have trouble understanding?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Yes, the way they interpret the method is nonsense to me. By definition (table 1.2.1), they said "Any axiomatic system contains a set of statements ....(3)....These are the axioms of the system." My question: if they are axioms, they must be correct, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, but they are only assumed to be true. A good example could be Classical Geometry. Euclid formulated geometry primarily relying on 4 axioms. The rest of his geometrical frame work then relied on a fifth axiom, the socalled parallel line postulate which essentially supposes that given a line and a point not on this line, then there is exactly 1 line that passes through this point, which doesn't meet the given line. However, the parallel line postulate can be modified to yield different geometries like hyperbolic geometry( more than 1 line which passes through the point and is parallel to the original line) and spherical geometry( no line that passes through the point and is parallel to the original line). So, what axioms we assume to be true, can radically alter our deductions and the results that follow.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0So, they give us the axioms (kind of given information, right?) and then 1 statement like theorem or corollary, We have to prove or disprove the theorem base on the given axioms, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, precisely. The axioms are the rules to the game. What outcomes come out of the game are entirely constrained by the axioms.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0in example 1.2.6. I don't understand the way they define {P,Q} <> z How?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Seems as though they are just making a map between the {P,Q,R} and {x,y,z}. They made the decision arbitrarily to show that its not an isomorphism.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I must say I didn't really read everything and I'm just going off my gut.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Whatever it may be, it follows from the relations they have established for Fe's and Fo's

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Why do they do that? They tried to prove that the example 1.2.5 and 1.2.6 is not an isomorphism, right? Is it not that it is trivial? In 1.2.5, only 3 relationships are constructed while there are 6 of them in 1.2.6. They are not isomorphism at the first look. right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0That is the reason why I don't understand the way they interpret the method. :)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0Thanks a ton for being here to help me out. I feel better now.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No problem, I'm actually studying the same sort of topic (Algebra and Analysis) for this semester. I have to get off now, but perhaps I may get on later and look further into your text.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0What kind of analysis? I am taking complex analysis this semester.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, its really a "preAnalysis" course, here its called advanced calculus. The algebra course is entitled abstract algebra, both are standard upper level undergraduate courses for those pursuing mathematics.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0hehehe. good luck. I took both them last year.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks, good luck to you as well.
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