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1

A statement such as $a>b<c$ could be useful if $a$ and $c$ are not contestants. I would interpret it as $a>b\ \mathrm{and}\ b<c$, i.e. $b<\min(a, c)$. In general, I'd interpret a statement of the form $a★b‡c$ as $a★b\ \mathrm{and}\ b‡c$. I'm pretty sure this is also how Python does it, for example.

0

"By default", all chained inequalities can be considered as illegal, because from an computer scientist's point of view and assuming that $<$ is left-associative: $a<b<c$ simplifies to $\text{\{True or False\}} < c$ which does not make sense ("type error"). To get around this, one defines the allowed combinations and their "expanded forms" as ...

2

In class I define the matrix product by $(AB)_{ij} = \sum_{k = 1}^{q}A_{ik}B_{kj}$ where $A$ is $p \times q$ and $B$ is $q \times r$. In my experience what causes the most confusion is not the subscripts indicating the component, but the meaning of the summation notation. Students do not identify the written formula with \$(AB)_{ij} = A_{i1}B_{1j} +A_{i2}B_{...

3

As you realize, this In my brief experience, I’m finding that my written diagrams or notations are not ideal. Admittedly, I will draw operators, numerals, and arrows on-the-fly, and they don’t always clearly communicate the process, especially when looking at them a few days later. is part of your problem. I suspect you may have difficulty ...

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