@Mathowitz Thank you! When talking about reflex angles, we need this word! And I have (wrongly) told my students that we don't have a such a word.
Here is another useful word about angles: goniometer.
@VivekGRamaswamy You have misquoted. He said “the greatest *terrorist* threat to our homeland is white supremacy.” China and fentanyl are different kinds of threats.
@thomasahle@pgeerkens@solidangles@matthematician In the real numbers 0/0 is indeterminate whereas 2/0 is undefined. In the real projective line, 2/0 = ∞, 2/∞ = 0, and ∞/2 = ∞; but 0/0 is still indeterminate and we have more indeterminate forms: ∞ - ∞, ∞/∞, ∞ 0.
@pgeerkens@solidangles@matthematician For the Ancient Greeks 0 was not a number but rather the lack of number. Many of our students think this way. (Ask them whether 0 is even, odd, neither, or both.)
As the concept of number expands, why shouldn't we call infinity a number? Cantor did.
@pgeerkens@solidangles@matthematician Aristotle distinguished potential from actual infinity. Mathematicians often imagine a potentially infinite process has completed: e.g. 1/3 = 0.3333... only if we imagine an infinite string of 3's on the right.
Lakoff calls this the Basic Metaphor of Infinity.
@Atheodosus @solidangles@matthematician The extended real line and the real projective line are both distinct definite entities. They contain all the real numbers and then one or two more numbers.
The former is topologically equivalent to a segment and the later to a circle.
@lightediand @matthematician The real projective line, the Riemann sphere, and the extended real line all include the number that you circled. The extended real line also includes -infinity.
Cantor, of course, had lots of different infinities!
@TomKenyon1@drrajshah The students have already seen v'= Av as a shorthand for a transformation.
For a problem, it might be better to start in two dimensions. And the algebra is challenging, so might be motivating first to do a numerical example that works out nicely.
@MeidasTouch Misplaced modifier. You mean: "Trump removed, in May 2018, the regulations that would have prevented the Silicon Valley Bank crash last week."