>A particular notorious example is the use of “It follows easily that” and equivalent constructs. It means something like this:
>One can now check that the next statement is true with a certain amount of essentially mechanical, though perhaps laborious, checking. I, the author, could do it, but it would use up a large amount of space and perhaps not accomplish much, since it'd be best for you to go ahead and do the computation to clarify for yourself what's going on here. I promise that no new ideas are involved, though of course you might need to think a little in order to find just the right combination of good ideas to apply.
Even knowing this ahead of time, this kind of thing can be maddening. Namely, when the meaning of the assertion is be sensitive to little sign changes, index shifts and the like these are quite likely to end up in the computation.
My Basic Concepts of Mathematics teacher was notorious for getting about halfway through a problem before announcing "and from here it's trivial to show...". One day he walks into class one day and addressed us:
"I've been told by the head of the department that I can no longer say 'it's trivial'. You have to understand when I say 'it's trivial', I just mean that I can do it"
>A particular notorious example is the use of “It follows easily that” and equivalent constructs. It means something like this:
>One can now check that the next statement is true with a certain amount of essentially mechanical, though perhaps laborious, checking. I, the author, could do it, but it would use up a large amount of space and perhaps not accomplish much, since it'd be best for you to go ahead and do the computation to clarify for yourself what's going on here. I promise that no new ideas are involved, though of course you might need to think a little in order to find just the right combination of good ideas to apply.
Even knowing this ahead of time, this kind of thing can be maddening. Namely, when the meaning of the assertion is be sensitive to little sign changes, index shifts and the like these are quite likely to end up in the computation.