4 ms·
> (1,2) + (2,4) - can't be done. are you talking about points or open intervals? the notation is ambiguous ;) but addition of points is fine if you look at the
by uryga 6y ago
> (1,2) + (2,4) - can't be done.
are you talking about points or open intervals? the notation is ambiguous ;) but addition of points is fine if you look at them as vectors
> a^2 + a^2 - fine. a^2 + a^3 - nope. a^2 + b^2 - nope.
what's wrong with the 2nd and 3rd ones? the 3rd one looks like half of Pythagoras theorem which is widely considered "fine" afaik ;)
- wcarey 6y agoIndeed. And if they're cartesian vectors, you're good. But if that second number is an angle measured in radians, you use yet a different set of rules for the addition. The conversation with 16 year olds when you explain that their previous teacher who told them that you couldn't add points wasn't lying, but was, perhaps oversimplifying things to make their life easier, is a fun and fraught one. I've had to reason kids through the fact that a^2 + b^2 is not equal to (ab)^2 or even (a+b)^2 more times than I can count. What's particularly difficult is that, confronted with the fact that 25 and 49 are manifestly different numbers, many still cling to the rule that a^2 + b^2 = (a+b)^2, because of the "law of distribution", which they haven't learned as the "law of distribution of multiplication of monomials over addition, and only that".
- CydeWeys 6y agoHow did I go all of my life so far without hearing the super useful word "monomial"? It's such an obvious concept to have a meaningful name, and yet I don't recall anyone ever having said that word.
- wcarey 6y agoI also didn't encounter it until I was relatively older. Our school has been pushing to introduce more rigorous language and definition in our 7-12th math program. For some students, it really seems to help. For others, it's really hard.