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Fair points. I was basing my terminology off of this table, after realizing that I had used incorrect terms. http://en.wikipedia.org/wiki/Contraposition#Compar
by trobertson 16y ago
Fair points. I was basing my terminology off of this table, after realizing that I had used incorrect terms.
http://en.wikipedia.org/wiki/Contraposition#Comparisons http://en.wikipedia.org/wiki/Contraposition#Comparisons
> If it is meant to be a synonym of what I'm calling negation [1], it would be "- (a * b)" for whatever you mean with " * ". However, this is by no means equal to "(-a) * (-b)".
This is absolutely correct, and was what originally prompted my comment. In your original comment, you say that
> The correct negation is: "we shouldn't work hard on getting our proofs correct."
which, if we let a = "should work" and b = "getting proofs correct", would mean that you said (-a) * (-b) is the negation, as opposed to -(a * b). By the quoted text, the negation would be either (-a) * b, or a * (-b).
This distinction is what I was trying to communicate, though it seems I did a poor job of that.
- vog 16y agoOkay, so your " * " operator means "implication" [1], because the terms "inverse", "contradiction" and "contrapositive" in your mentioned Wikipedia article refer only to implications. However, the original statement isn't an implication. Also, neither your proposed part "should work" nor the other part "getting proofs correct" are logical statements. Those are just parts of a sentence. In other words, your decomposition doesn't make any sense. [1] That is, "a * b" = "if a then b" = "from a follows b" = "a implies b"