Christian Lawson-Perfect
Follow

How do you feel about lines like this:

\[ a = b < c = d \]

If you're skim-reading, and the terms a,b,c,d are quite long, you might not notice the < in the middle, and think that a = d. Is there a better way?

@christianp If the terms are long, I'd prefer it to be broken up into separate lines: (Hoping this renders correctly)

\(\begin{align*}a &= b\\&< c\\&=d\end{align*}\)

@christianp If the terms are short, you might be as well stating it in prose rather than symbolically.

@j @christianp yes, this is the right way to do it. Analysis often uses long chains like this, alternating between rearrangement/rewriting (=) and applying estimates (<, etc.), which would be way too verbose if written out step-by-step.

@christianp It's perfectly fine to me, but then I'm used to reading crazy stuff in code. Are brackets an answer? (a=b) < (c=d)

@jsmall no, this isn't code: it's maths. The correct interpretation of the line is a<d.

@jsmall brackets grouping the equalities would help, but might hide the point of the statement, which is that the first term is less than the last one

@christianp @jsmall I tend not to be able to skim math papers at all, so it's a bit "I have 99 problems and single line proofs ain't one"

@christianp @bremner I've never say never. But in terms of "correct interpretation", aren't a < c and b < d just as correct?

@jsmall @bremner yes, but the point is to show the working-out: while it might be clear that a=b and b<c, it might not be obvious that a<c.

@christianp @jsmall I agree that such lines generally serve mainly to jog the memory as to how the actual proof goes than being self contained proofs.

@christianp @jsmall To amplify, it really depends on the audience and the desired level of exposition. I've seen math texts that present things in that form, but of course it's not great for actually teaching. On the other hand, it is pretty easy to reconstruct a convincing proof given that roadmap, and for some people that's good enough.

@christianp skim-reading that, my mind automatically went "a is equal to b, which is less than c, which is equal to d"... So I guess I don't have that issue

Things get funkier when you see stuff like a = b == c in certain code though

@btcprox that was easy to skim-read. It's harder if a,b,c and d are really long - the relation symbols in the middle are easy to lose

@christianp fair enough, then I'd agree with what @j said, to either elaborate in prose if short enough, or to go about \align-ing with the relational symbols

Sign in to participate in the conversation
Mathstodon

A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.

Use \( and \) for inline LaTeX, and \[ and \] for display mode.