celtschk
Reputation
14,253
Top tag
Next privilege 15,000 Rep.
Protect questions
 Mar 24 awarded Necromancer Mar 3 awarded Revival Feb 26 awarded Necromancer Feb 24 awarded Necromancer Feb 18 awarded Necromancer Jan 22 awarded Notable Question Jan 18 answered Why does a matrix with zero eigenvalues and nonzero singular values have to be non-symmetric? Jan 17 comment Less suggestive terms for “vector addition” and “scalar multiplication” It's also quite uncommon to denote a maximum with $\min$ ☺. I guess you wanted to write "minimum" here. Jan 17 revised How to compute $\cos(\arctan(2)) = 1/\sqrt{5}$ fixed math formatting and spelling Jan 17 comment Let $2 = \{ 0, 1 \}$ and $X$, $Y$ be sets. @GitGud: I disagree. The best definition of 2 is still "the successor of 1". Of course if you model the natural numbers with the von-Neumann construction, the successor of 1 turns out to be $\{0,1\}$. But that's already a result, not the definition. Jan 17 revised Taylor expansion of $\cosh^2(x)$ fixed MathJax formatting Jan 17 comment Function with infinitely many right inverses? Indeed, with that method you can easily show that the set of right inverses can have any cardinality, by just replacing $\mathbb N$ with a set of the desired cardinality. Jan 17 comment a vectorspace, a linear map, the kernel and image of it @Bernard: I don't think the Babylonians defined whether $0$ belongs to the set of natural numbers. Peano defined the natural numbers both without and with $0$, and used the notation $N_0$ for the latter. So there's precedent for that notation as old as the axiomatization of natural numbers themselves. Jan 17 comment If the sets $A=\{x\in E, f(x)<\lambda\}$ and $B=\{x\in E, f(x)>\lambda\}$ are open, then $f$ is continuous Strictly speaking, you haven't covered open sets like $(a,b)\cup (c,d)$. OTOH, the empty set is already covered by $(-\infty,b)\cap(a,\infty)$ through the case $a\ge b$. Jan 17 comment Proving that basis always exists and is not unique Of course to prove non-uniqueness for dimension $>1$ (the precondition to having two basis elements $e_1,e_2$ to begin with), you can also just replace $e_1$ with $e_1+e_2$. That works even for $\mathbb F_2$. Jan 16 comment Is there a relationship between isometry as defined on metric spaces and those on vector spaces? "I look up the definition of isometry online and many sources tell me it is a bijective "structure preserving" map." That sounds more like the definition of an isomorphism. Now an isometry is an isomorphism, but in general an isomorphism is not an isometry. Jan 16 answered Probability of urns Jan 16 revised Any subspace of connected set is connected? added 5 characters in body Jan 10 comment In Wikipedia's motivating example of wedge product, what happened to $e_1 \wedge e_1$ @Bye_World: So "alternating" does not mean the same as "antisymmetric"? I thought the property you seem to call "alternating" is called "nilpotent". Jan 8 answered In Wikipedia's motivating example of wedge product, what happened to $e_1 \wedge e_1$