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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.
Nov
23
comment Is subtraction defined in $\mathbb{Z}_{2}$?
Subtraction is defined in any field.
Nov
20
comment Is there a field size such that it makes perpetual “candy crush”
The question seems underspecified. Do you want the cascade to definitely go on for the given length, or probably go on that long, or what? How is the trigger move chosen? And what kind of distribution are we drawing the initial field state from?
Nov
20
comment How many different ways can I get up a flight (of stairs) with 11 steps?
You've left out the key step, which is explaining why this definition of the $n$-th Fibonacci number is equivalent to whatever definition you originally learned (probably the inductive one). Without that, you're basically saying that the Fibonacci numbers are the answer because you redefined them to be the answer.
Nov
18
comment Are there any limit questions which are easier to solve using methods other than l'Hopital's Rule?
Well, limits that don't have indeterminate forms, like $\lim_{x \to 2}3$, are much easier to solve without l'Hopital's rule than with it.
Nov
17
comment Minimizing fuel usage for small boat between given points
Depending on the questioner's math background, it might also be plausible to use the AM-GM inequality to minimize $G$. $(8/V+V/50)/2 \ge \sqrt{8/V \cdot V/50} = 2/5$, with equality between the far-left and far-right when $8/V=V/50$. It's the kind of thing you might know at age 12 if you're into contest or recreational mathematics.
Nov
13
comment What is the maximum number of points of intersection of 8 circles?
Isn't 8P2 $56$?
Nov
9
comment Proof that a set is non-star-shaped.
Heck, you could just use the empty set. The definition of a star-shaped set requires it to contain at least one point.
Nov
9
comment What is ∃ in set theory?
I'm surprised you managed to get that symbol into your title without learning what it means in the process. The Google results for ∃ are decently informative, as are the results for backwards E.
Nov
8
comment Is there an example for an undefinable number?
What do you mean by "true" reals or "truly" uncountable?
Nov
6
comment Can any 3d rotation be done with only two angles?
Do we get to use a rotation twice? For example, rotating 90 degrees around the X axis, 90 degrees around the Y axis, and 90 degrees the other way around the X axis to create a 90 degree rotation around the Z axis?
Nov
3
answered Eigenvalues of reflection