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 1d comment Why does it have to be an integer? @HenningMakholm: The problem says $n$ and $k$ are greater than $1$ anyway. Apr 29 comment Absolute value graph sketching It's more like folding it across the $x$ axis, not reflecting it. Reflecting it would be negation; the positive parts would become negative as well as the negative parts becoming positive. Apr 28 comment Why do we classify infinities in so many symbols and ideas? Saying "infinity is just... infinity" is like saying that "big numbers are just... big", so why do we need separate numbers like 1 million and 3 billion? Apr 26 comment Is a ball always connected in a connected metric space? @mathguy: Is $(1, 0)$ not in the space? It's on the unit circle, and it's not the removed point (that's $(0, 1)$). Apr 13 comment Would an infinite random sequence of real numbers contain repetitions? @JingWang: You're only selecting countably many of them. Apr 10 answered How to prove independence is not a transitive relation? Apr 6 comment Tips on determining compact to non-compact sets "The disc includes the boundaries, yes?" - but in the punctured disc, the puncture is an additional part of the boundary. Mar 21 awarded Quorum Feb 24 comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald? @DCShannon: There can't be anyone standing in front of the first person, by the definition of "first". If there was anyone in front of the first person, one of them would be first. Also, the question is in the title, as well as restated in the body. Look at the parts with the question marks. Feb 23 comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald? @TTT: The problem statement does say the line "starts with person #1", so we're given the existence of at least one person in line. That might not be the case in the original problem the questioner was working on, but it's definitely the case in the problem as posted. Feb 19 answered A probability theory question about independent coin tosses by two players Jan 27 comment Solving a logarithmic equation that has an exception to the power rule @Tim: What "mod"? Jan 21 comment “Ordering” of Complex Plane The distance would generally be infinite, and space-filling curves must be self-intersecting, so you'd have to deal with that, too, but you could probably get an ordering relation out of it if you tried. It's just that "ordered field" means more than "a field with an order on it"; the ordering and the field structure have to be compatible in a specific way that won't hold here. Jan 14 comment Is $[p \land (p \to q)] \to q$ a tautology? You'll never be asked to solve the really hard cases, but the general problem of determining whether a proposition is a tautology is actually really hard. It's co-NP-complete, as its complement is (a slight variation on) boolean satisfiability; a proposition is a tautology if and only if there is no satisfying assignment of its negation. Jan 12 suggested rejected edit on Is a matrix multiplied with its transpose something special? Dec 22 comment Combinatorial argument for an identity That's the hockey-stick identity, isn't it? I've always found it really obvious from drawing the hockey stick in Pascal's triangle. Dec 10 comment Kernel in Modern Algebra The windspeed map is a problematic example, since there's a nonlinearity inherent in the $(\theta, s)$ representation. Depending on how you define things, the map from $(x, y, z)$ to $(\theta, s)$ isn't linear, or the $(\theta, s)$ space isn't a vector space, or vector addition in the $(\theta, s)$ space is weird. Dec 10 comment Prove that the following is not true or true. And how does this example disprove the statement? Particularly since it's an "exists" claim, not an "all" claim? Dec 9 comment Prove that the following is not true or true. How is that a counterexample? Dec 9 comment Must eigenvalues be numbers? And as a trivial explicit construction, for any $\lambda \in F$, the map that takes every $v$ to $\lambda v$ has eigenvalue $\lambda$, so every $\lambda \in F$ is an eigenvalue of some linear map.