daviddoji/CalculusWithJuliaNotes.jl
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Merge branch 'main' into v0.15

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jverzani 2023-03-28 11:02:38 -04:00
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quarto/precalc/calculator.qmd
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@ -326,7 +326,7 @@ $$
\frac{1 + 2}{3 + 4}?
$$
It would have to be computed through $(1 + 2) / (3 + 4)$. This is because unlike `/`, the implied order of operation in the mathematical notation with the *horizontal division symbol* (the [vinicula](http://tinyurl.com/y9tj6udl)) is to compute the top and the bottom and then divide. That is, the vinicula is a grouping notation like parentheses, only implicitly so. Thus the above expression really represents the more verbose:
It would have to be computed through $(1 + 2) / (3 + 4)$. This is because unlike `/`, the implied order of operation in the mathematical notation with the *horizontal division symbol* (the [vincula](http://tinyurl.com/y9tj6udl)) is to compute the top and the bottom and then divide. That is, the vincula is a grouping notation like parentheses, only implicitly so. Thus the above expression really represents the more verbose:
$$
@ -349,7 +349,7 @@ To emphasize, this is not the same as the value without the parentheses:
:::{.callout-warning}
## Warning
The viniculum also indicates grouping when used with the square root (the top bar), and complex conjugation. That usage is often clear enough, but the usage of the viniculum in division often leads to confusion. The example above is one where the parentheses are often, erroneously, omitted. However, more confusion can arise when there is more than one vinicula. An expression such as $a/b/c$ written inline has no confusion, it is: $(a/b) / c$ as left association is used; but when written with a pair of vinicula there is often the typographical convention of a slightly longer vinicula to indicate which is to be considered first. In the absence of that, then top to bottom association is often implied.
The vinculum also indicates grouping when used with the square root (the top bar), and complex conjugation. That usage is often clear enough, but the usage of the vinculum in division often leads to confusion. The example above is one where the parentheses are often, erroneously, omitted. However, more confusion can arise when there is more than one vincula. An expression such as $a/b/c$ written inline has no confusion, it is: $(a/b) / c$ as left association is used; but when written with a pair of vincula there is often the typographical convention of a slightly longer vincula to indicate which is to be considered first. In the absence of that, then top to bottom association is often implied.
:::
@ -424,7 +424,7 @@ To confuse things even more, consider
2pi^2pi
```
Is this the same as `2 * (pi^2) * pi` or `(2pi)^(2pi)`?. The former would be the case is powers had higher precedence than literal multiplication, the latter would be the case were it the reverse. In fact, the correct answer is `2 * (pi^(2*pi))`:
Is this the same as `2 * (pi^2) * pi` or `(2pi)^(2pi)`? The former would be the case is powers had higher precedence than literal multiplication, the latter would be the case were it the reverse. In fact, the correct answer is `2 * (pi^(2*pi))`:
```{julia}