Hi

[balmy ridge]

Hi,How formalise analysis ,synthesis reasoning

[grand olive]

any particular question?

[balmy ridge]

direct reasoning : P and (P implie Q) is equivalent logicaly to Q

absurd reasoning : (P implie Q and P implie non Q )implique Q

So analysis-synthesis reasoning : ?

@grand olive

[grand olive]

(Q->P) and (P->Q) -> (Q<->P)

[balmy ridge]

I didnt understand .

[grand olive]

https://math.stackexchange.com/questions/2268340/analysis-synthesis-reasoning

[balmy ridge]

It's a bit more complex

analysis synthesis reasoning , aquiere solutions and for thouse solutions conditions .

[grand olive]

have u done if and only if proofs

you are just proving in double directions

[balmy ridge]

Yes P is equivalent to Q ; P is equivalent to P1 equivalent to P2 equivalent to P3 ..equivalent to Q

So P equivalent to Q .

[grand olive]

yes that is analysis-synthesis reasoning mathematically

[grand olive]

This line of implication

[balmy ridge]

Yes , but it's not equivalence

it's logical equivalence .

[grand olive]

not logical equivalence itself

so it is a method to justify the equivalence

so in essence, analysis-synthesis is a method to prove logical equivalence

[balmy ridge]

in bibmath ; Analysis: We assume that the object exists and try to find the necessary conditions that this object must satisfy. In doing so, we prove that if the object exists, it must necessarily be equal to a certain object
𝑂
O (this ensures its uniqueness).

Synthesis: We consider the object
𝑂
O identified in the analysis section and verify that it indeed possesses the desired properties (this ensures its existence).

[grand olive]

hmm this seems to be a different use

i havent seen analysis and synthesis for existence and uniqueness

yeah logic is eating my mind alive, i hope someone else can takeover