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/sci/ - Science & Math

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9567715 No.9567715 [Reply] [Original]

mfw "proof by contradiction"

>> No.9567723

>>9567715
Why?

>> No.9567727

>>9567723
>proof
Why not?

>> No.9567738

>>9567715
Ok, so you wanna prove P->Q:

If you prove the opposite of (P->Q) is always false, then P->Q itself is always true.

So what's wrong with that anon?

>> No.9567743

>>9567738
Some people agree that proving that something doesn't work one way doesn't mean it works the opposite, but other ways. However in our time proof by contradiction is known as valid.

>> No.9567745

>All functions are continuous.
Constructive mathematics was a mistake.

>> No.9567748

>>9567738
>>9567743
It works like: You prove the opposite is false, it doesn't mean the premise is true, it just states that the opposite is false and has nothing to do with the original premise.

>> No.9567749

>>9567743
idiot

>> No.9567751

>>9567743
When you are proving something cannot exist, proof by contradiction is assuming it can exist, then proving a logical inconsistency. Therefore, there was a poor assumption somewhere, which is that the thing can exist. Therefore, it cannot exist.

It is not doing a mythbuster approach saying "well, we couldn't do it this way so it must be impossible."

>> No.9567753

>>9567745
What?

>> No.9567758

>>9567753
If you reject proof by contradiction, then you reject the law of excluded middle (and thus the axiom of choice as well). Mathematics without lem is called constructive mathematics, and in certain models of constructive mathematics, all functions are continuous.

>> No.9567764

>>9567743
A statement being a contradiction means it's false under all possible conditions.

Therefore the opposite of that given statement would be a Tautology which means that it's true under all possible conditions.

>> No.9567765

>>9567738
What's the 'opposite' of P->Q? P->Q'?

>> No.9567775

>>9567758
>certain models
AKA, also rejecting the set theoretical definition of a function. Also they don't "reject it", they just don't take it as an axiom, law of thought.

>> No.9567776
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9567776

>>9567765
( P -> Q ) is equivalent to ( !P v Q )
(You can get the CNF from the truth table if you're not sure about it.)

Therefore the opposite of P -> Q:
!( P -> Q ) is equivalent to !( !P v Q )
which is equivalent to (P ^ !Q) according to DeMorgan's law.

TL;DR
(P ^ !Q)

>> No.9567785

>>9567775
Well, yes. Rejecting an axiom means that you don't accept/use it. It doesn't mean that you assume that it's incorrect or whatever you're trying to imply it does.

>> No.9567789

>>9567785
Yea, and still, most of real anal is perfectly constructiblr.

>> No.9567793
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9567793

>>9567751
>which is that the thing can exist.
what if one of your axioms that underlie what you mean by e.g "existing" are "wrong"?

>> No.9567800

>>9567793
What axiom underlying existing? Are you talking math anymore or philosophy with what it means to exist?

>> No.9567817

>>9567800
I have nothing concrete.
But when you say "Assume that X is Y", you are working in some axiomatic system, and what if the contradiction arises due to a problem with the system you are working in?

>> No.9567822

>Proof requires induction
DROPPED

>> No.9567823

Did we come to any conclusions then?

>> No.9567825

>>9567822
Everything requires induction

>> No.9567942

>>9567745
That's literally a good thing

>> No.9567946
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9567946

>X=>B
>-X=>B
Where X is unknown.

>> No.9567988

>>9567776
P -> Q / ~P | Q / ~(~P | Q ) / P & ~Q
https://programming.dojo.net.nz/study/truth-table-generator/index

>> No.9568069

>>9567738
The explanations of proof-by-contradiction in here are neglecting the distinction between that and proof-by-negation, which is only fine if you're working in brainlet classical logic.

>> No.9568076
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9568076

>>9568069
There is no difference, and classical logic is suspect as well.

>> No.9568108

>>9567789
>can't show surjection iff right inverse
>perfectly constructible
sure bud

>> No.9568120
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9568120

>>9567946
This was amazing. So original. Who came up with it? This is real math. And the originator deserves credit.

Oh, probably not a jew, lets ignore this type of proof. Not suspect at all.

>> No.9568377

>>9567825
Prove that induction is possible.

>> No.9568397

>>9567823
Yes.
OP is a brainlet.

>> No.9568410

>>9567764
>Therefore the opposite of that given statement would be a Tautology
No, because in constructive mathematics there is no law of excluded middle: you can't assume that either p or ~p is true.

>> No.9568553

>>9567715
>calls it a proof by contradiction
>Its actually a proof by contrapositive
90% of the god damn time

>> No.9568802

>>9567817
Then no proof would be valid. Are you legitimately retarded?

>> No.9568841

>>9568802
yes but how would we know the proofs are not valid if we are yet to discover any issues?