Most of the time I’ve run into the word “obviously” is in the middle of a proof in some textbook, and my understanding of the word in that context is that it means “the justification of this claim is trivial to see, and spelling it out would be too tedious/would disrupt the flow of the proof.”
I assert that it (“obviously” in math) is most often used correctly, but that people spend more time experiencing it used incorrectly—because they spend more time thinking about it when it is not obvious.
Most of the time I’ve run into the word “obviously” is in the middle of a proof in some textbook, and my understanding of the word in that context is that it means “the justification of this claim is trivial to see, and spelling it out would be too tedious/would disrupt the flow of the proof.”
I thought the mathematical terms went something like this:
Trivial: Any statement that has been proven
Obviously correct: A trivial statement whose proof is too lengthy to include in context
Obviously incorrect: A trivial statement whose proof relies on an axiom the writer dislikes
Left as an exercise for the reader: A trivial statement whose proof is both lengthy and very difficult
Interesting: Unproven, despite many attempts
Well, that’s what it’s supposed to mean. One of my professors (who often waxed sarcastic during lectures) described it as a very dangerous word...
Do you really assert that it is more often used incorrectly (that the fact is not actually obvious)?
I assert that it (“obviously” in math) is most often used correctly, but that people spend more time experiencing it used incorrectly—because they spend more time thinking about it when it is not obvious.
No, I guess not.