So, I was was thinking the other day. As a side effect of thinking, I have proven that not only can you compare apples to oranges, apples ARE oranges. Because:
Apples = Not Oranges
Simple enough, Apples are not oranges.
Not Oranges ≠ Apples
Not all fruits that are not oranges are apples. Again, pretty simple.
Apples ≠ Not Oranges
Here’s where it gets tricky. Since Not Oranges ≠ Apples, this makes our original statement (Apples = Not Oranges) false. This is because in order to use an equal sign correctly, the statement must be true whether the equation is reversed or not ( A = B, B = A or 2/1 = 2, 2 = 2/1)
Apples = Oranges
Getting rid of the double negative in the equation leaves us with this, proof that Apples do in fact, equal oranges.
Now I know that this is probably bad math, but it’s fun to think about :D.
Arg… -head assplodes-
That kinda reminds me of: http://www.stacken.kth.se/lists/best-forestry/2001-05/jpg00000.jpg
So, yeah. I was talking about http://en.wikipedia.org/wiki/Affirming_the_Consequent in the IRC.
Nofirefrog, I think that you may be onto the general problem with this equation. But, In that article, affirming the consequent is defined as:
If P, then Q.
Q.
Therefore, P.
Mine doesn’t really even (try to) take on an argument form like that:
A = O
O ≠ A
∴ A ≠ O
The last part of the statement is just simplified from the double negative.
Correct me if I’m wrong, but I don’t think “Affirming the consequent” applies.
You can apply it in the same sense. Just a bit differently.
If P, then Q. Q therefore, P. This can be stated as: If P, then not Q. It would follow that by this whole affirming the consequence thing that you couldn’t say If Q, then not P. And, even if we don’t have to agree on that there is a more simply problem with this. I see the justification, but mathematically you cant transition from A = O to O != A (coding ftw :D). It just doesn’t make sense.
If you want to go into proving that two things that aren’t the same, but they really are then ask me for the proof that 1 = 0.
I think I see what you’re saying.
But, mathematically, A = O never existed because O != A.
What I’m saying is because Not Oranges ≠ Apples, I make my first sentence false. Because my first sentence is invalid, I create a statement that is valid when compared with the second statement, thus, Apples ≠ Not Oranges.
I just no realized, though, that because I just created a third sentence that is valid with my second sentence, I created yet another false sentence. And, being that there is no other sentence I can create with the variables I used, it renders my second sentence useless.
Basically I am unable create a whole valid statement with the second sentence. So… it’s moot. :(
You know, I never really liked either of them….
There are a few problems here, but most important is that you’re misusing ‘=’. What you really want in this case are set operations - Apples are a subset of the not-oranges set, but are not equal to it - tables and cats are also members of this set, yet are distinct from apples.
Phil is right. Apples are not oranges, but so are a ton of things. You could use the same proof to show that a pear doesn’t equal not an orange, and you’d be right. It’s a part of the “not orange” group, not the whole thing. It’s like saying that 1 =/= 1-9. It’s true, because 1 is just a part of 1-9. You could say that 1=2-10 by the same logic that you used above, simply because it is flawed.
Phil is correct, thats not how Maths work.
Apples ⊆ Not Oranges (Apples are a subset of Not Oranges)
Therefore
Not Oranges ⊇ Apples (Not Oranges are the superset of Apples)
and we all know
Oranges ⊄ Not Oranges, and Oranges ≠ Not Oranges (Oranges are not a subset of Not Oranges, nor are they Not Oranges)
Thus
Apples ≠ Oranges
Maths win!