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/sci/ - Science & Math

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10991381 No.10991381 [Reply] [Original]

Is a "derivation" mathematically the same as a logical implication? Like can a derivation be respresent as P => Q? Or is it more like P => a => b => Q?

>> No.10991849

>>10991381
If p arrow a, and a arrow b, and b arrow q, then yes p really does arrow q.

>> No.10991853

>>10991381
Derivations aren't even a thing outside of human language. It's all implications or the lack thereof.

>> No.10991856

>>10991381
Yeah. Given a set of premises you derive a conclusion/result.
You usually use derivation for formulae, but there are exceptions

>> No.10991862

pic related... is this going to be into your fridge and being re-used for the rest of times ?

fuck ups happens.

>> No.10991973

>>10991849
Congratulation, you just unlocked transitivity

>> No.10991997

>>10991849
>>10991973
Right I know technically it's transitive but a and b are more or less the steps in the derivation and P would be our proposition and Q is our conclusion. So would that be an adequate way of describing how it works?

>> No.10992183

>>10991997
exactly transitivity

>> No.10992337

>>10992183
So are you saying a derivation is where transitivity exists?

>> No.10992364

It's just iff and only iff chains

>> No.10993377

My experience is that a derivation is usually called some procedure which will show you that it is reasonable to believe some theorem is true and bother to prove it. In that it is not P=>Q but rather something along the lines Q=>A, P=>A, so maybe P=>Q

So you first derive a result which will give you an idea that it is true, and then you mathematically prove it.

In many lectures, mostly physics, only derivations are presented