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Martin Sleziak
Martin Sleziak
12:05 AM
@MartinSleziak I think I'd intended "geometric" to mean right-triangle trig, so that "geometric and circular" was intended to encompass trigonometry both as it appears in U.S. secondary school geometry and in U.S. secondary school advanced algebra / algebra 2 / precalculus. I doubt I'd intended to include hyperbolic trig, though probably because I wasn't even thinking about it, not because I intended to exclude it. — Isaac 4 hours ago
That is to say, I'd expect the tag to be used for 1 and 2, and I wouldn't have thought about the tag in relation to 3 and 4, but have no immediate objection to its use that way. — Isaac 4 hours ago
 
 
3 hours later…
Martin Sleziak
Martin Sleziak
3:29 AM
A new tag dedekind-cuts. Keep? Remove?
4
Q: How to prove that the both definition of completeness of $\mathbb{R}$ are equivalent?

onurcanbektasIn the definition of completeness of a set, in particular $\mathbb{R}$, I have seen the following definitions: Dedekind: Every non-empty bounded of subset has a least upper bound (with respect to $\leq$). Cauchy: Every Cauchy sequence converges. However, how can one prove that both ...

real-analysis real-numbers cauchy-sequences complete-spaces dedekind-cuts
 
 
11 hours later…
Martin Sleziak
Martin Sleziak
2:02 PM
Another new tag is pseudo-euclidean-spaces.
0
Q: Decomposition of a vector in Pseudo-Euclidian space into to form $x = \lambda z + y$, where $(z,y) = 0$ and $\lambda = -(x,z) $

onurcanbektasIn the book of Linear Algebra by Werner Greub, at page 284, it is given that More generally let us consider an n-dimensional pseudo-Euclidean space with index -1. Then every fixed time-like unit vector z determines an orthogonal decomposition of E into an (n-1)-dimensional subspace cons...

linear-algebra vector-spaces metric-spaces pseudo-euclidean-spaces
 

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