Timeline for Is it considered a mistake to use different correct notation for writing intervals?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 6, 2022 at 2:20 | comment | added | Daniel R. Collins | We have different standard words for the different concepts of "path" vs. "interval", and I'm not sure it's helpful to say that sometimes they can be mashed together in any way. | |
| May 6, 2022 at 0:07 | comment | added | kcrisman | Hopefully clarified previous sloppiness on "line" versus "path" integrals. | |
| May 6, 2022 at 0:03 | history | edited | kcrisman | CC BY-SA 4.0 |
clarified type of integral and notation
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| May 5, 2022 at 23:51 | comment | added | kcrisman | It's presumably been even longer since I thought about line integrals, but that is what I was thinking of. I'll try to clarify my answer. | |
| May 5, 2022 at 16:52 | comment | added | Xander Henderson♦ | But in complex analysis, it is well understood that $\int_{\gamma}$ denotes the integral over some parameterized curve. It has been a while since I've thought about complex analysis, but you get something like $$\int_{\gamma}\,\mathrm{d}z = \int_{a}^{b} \gamma'\,\mathrm{d}t, $$ where $\gamma : [a,b] \to \mathbb{C}$ is a continuously differentiable curve. | |
| May 5, 2022 at 16:50 | comment | added | Xander Henderson♦ | The interval $-(2,3)$ is, in most contexts, the same as $(-3,-2)$ (more generally, if $A\subseteq \mathbb{R}$, then $$-A = \{ -x : x\in A\},$$ which is not the same as just changing the orientation of an interval). Integrating over sets also typically implies that it is the Lebesgue integral which is being considered, rather than the Riemann integral, and there is no real notion of "orientation" for the Lebesgue integral. I will agree, however, that if $\alpha,\beta\in\mathbb{C}$, then $$\int_{[\alpha,\beta]} f(z)\,\mathrm{d}z = -\int_{[\beta,\alpha]} f(z) \,\mathrm{d}z.$$ | |
| May 3, 2022 at 12:34 | history | answered | kcrisman | CC BY-SA 4.0 |