- #1
charlie_sheep
- 4
- 0
I've just started studying college math.
I read the proof by contradiction is based on the law of excluded middle. So i tried
to make a general logic structure of this kind of demonstration to see how it could use
this law. If I'm right, of course.
Let X and Y be propositions.
1. X -> Y
2. ~Y
3. X v ~X ¹
By 1 and 3 we have:
4. Y v ~X
By 2 and 4 we have:
~X
Q.E.D.
¹ - Law of excluded middle
Is this how reductio ad absurdum is made?
I mean, generally the following statement is used:
"Suppose X is true. Then Y is true. But Y is false. So X is false."
But isn't it the same thing i just did above?
I know that, probably, I'm just talking non-sense. But even so, i think this non-sense
can help you guys to help me out with my doubts.
Anyway, thank you for the attention.
My first language is portuguese and I'm not a good english writer. So if i made any english mistakes, i apologize.
I read the proof by contradiction is based on the law of excluded middle. So i tried
to make a general logic structure of this kind of demonstration to see how it could use
this law. If I'm right, of course.
Let X and Y be propositions.
1. X -> Y
2. ~Y
3. X v ~X ¹
By 1 and 3 we have:
4. Y v ~X
By 2 and 4 we have:
~X
Q.E.D.
¹ - Law of excluded middle
Is this how reductio ad absurdum is made?
I mean, generally the following statement is used:
"Suppose X is true. Then Y is true. But Y is false. So X is false."
But isn't it the same thing i just did above?
I know that, probably, I'm just talking non-sense. But even so, i think this non-sense
can help you guys to help me out with my doubts.
Anyway, thank you for the attention.
My first language is portuguese and I'm not a good english writer. So if i made any english mistakes, i apologize.