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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.