Timeline for Can the differential be unitless while the variable have an unit in integration?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 6 at 11:44 | audit | First answers | |||
| Jul 6 at 11:56 | |||||
| Jul 6 at 6:55 | comment | added | YiFan Tey | @XanderHenderson I don't think that explanation is correct. The distinction is between probabilities and probability densities; the point is that $f(x)$ is not a probability (and hence cannot be written in percentages) --- which would indeed be dimensionless --- but is instead a probability density. | |
| Jul 6 at 6:33 | comment | added | DannyNiu | @XanderHenderson Not to insist on arguing, but for most of the time, I just assume the percentage symbol % has the unitless value of 0.01. It's multiplied with a human-friendly 2-digit number (occasionally 1-digit or 3-digit) to indicate progress or fraction. This way, "%" is generic, and the "amount per 100" can be per 100 whatever the author wishes. | |
| Jul 5 at 19:36 | comment | added | Prem | Like I said in my answer , that is not the only way to resolve this issue , @XanderHenderson , there are authors who will use things like "Let $x$ be the length" where $x$ must itself be length units , while there are other authors who will use things like "Let $x$ be the length in meters" where the real number $x$ itself is unitless. With that way , it is then more meaningful to consider $E[x^2+x^3]$ with "Unitless Percentages" , otherwise , we can not add area to volume. | |
| Jul 5 at 18:54 | comment | added | Xander Henderson♦ | @DannyNiu Remember that "percent" is amount per 100. Per 100 whats? Oh, per 100 of whatever $x$ is. Hence if you are thinking of $f(x)$ as a percentage, then it has units of $1 / (100[x])$. | |
| Jul 5 at 10:33 | history | edited | Abezhiko | CC BY-SA 4.0 |
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| Jul 5 at 7:38 | comment | added | DannyNiu | Thanks. The unit of the density function is what I've missed. Too often $f(x)$ was thought in percentage - i.e. unitless. | |
| Jul 5 at 7:36 | vote | accept | DannyNiu | ||
| Jul 5 at 7:34 | history | answered | Abezhiko | CC BY-SA 4.0 |