Activity for leovt
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Edit | Post #286692 | Initial revision | — | over 2 years ago |
| Answer | — |
A: Notation for nested exponents The power operation is considered right-associative, because the left-associative interpretation would just be a more complicated notation for the product of the exponents: $a^{bc} = (a^b)^c \neq a^{b^c} = a^{(b^c)}$ Similar arguments lead to the same interpretation for higher towers, where it ... (more) |
— | over 2 years ago |
| Edit | Post #283717 | Initial revision | — | about 3 years ago |
| Answer | — |
A: How does counting E twice explain the discrepancy between the third between C and E, third between E and G v. fifth between C and G? The discrepancy comes from the way musical intervals are named. Image alt text The names are derived from the number of "fenceposts" including the first one, where as the corresponding length of the fence is one unit shorter. The third+third=fifth equation is thus not $$3+3=5$$ but $$(3-1) + (3... (more) |
— | about 3 years ago |
| Comment | Post #283317 |
@#52996l yes exactly, thanks. I hope the edited answer is clearer now. (more) |
— | about 3 years ago |
| Edit | Post #283317 |
Post edited: Tried to explain more clearly after feedback in the comment. |
— | about 3 years ago |
| Comment | Post #283332 |
You are correct that it is possible to define the length using finer and finer grids, my point was not that this is impossible. My point is that you have to be careful to get a good definition of arc length this way. (For the area you do not need as much care, the little errors at the border will ten... (more) |
— | about 3 years ago |
| Edit | Post #283332 | Initial revision | — | about 3 years ago |
| Answer | — |
A: How do mathematicians measure shape perimeters? A main idea mathematicians use to define lengths of curves, areas of flat shapes, volumes of solids etc is to divide them into smaller and smaller parts such that 1. The finer and finer subdivisions approximate the shape better and better. 2. The measure of the small parts is already defined. ... (more) |
— | about 3 years ago |
| Edit | Post #283317 |
Post edited: |
— | about 3 years ago |
| Edit | Post #283317 | Initial revision | — | about 3 years ago |
| Answer | — |
A: In $w_{k + 1} - w_k = (\frac{1 - p}{p})^{exponent}(w_1 - w_0)$, why isn't exponent $k + 1$? If you set $k=0$ the equation becomes $$w{0+1} - w0 = r^{\textrm{exponent}}(w1-w0)$$ For this equation to hold (in general) the exponent must be zero and not one. Thus an exponent of $k+1$ must be wrong. I think the problem is not a fence-post problem but the proper base case for the induction... (more) |
— | about 3 years ago |
| Edit | Post #282396 |
Post edited: do not assume boss is "he" |
— | over 3 years ago |
| Edit | Post #282396 | Initial revision | — | over 3 years ago |
| Answer | — |
A: How to visualize division as splitting Dividend into B equal “partial groups”, then rounding up A partial groups to get a full group? The bolded sentence confuses $A$ and $B$, it should be: Meanwhile, $X \div \frac{A}{B}$ means starting out with a total of X items, splitting it up into A equal "partial groups" (where a full group is actually B of these partial groups), and then rounding up B partial groups to get a full group. ... (more) |
— | over 3 years ago |