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1d
comment Proving that one has solved chess by exhibiting the zeroes of polynomials over finite fields?
Scott Aaronson has a stackexchange account. I just sent him an email since I figure he might be well equipped to answer a question about what he meant on his blog.
2d
revised Can someone explain why $(e,1)$ and $(t, \ln t)$ are the two points of intersection for this question?
added 219 characters in body
2d
comment Can someone explain why $(e,1)$ and $(t, \ln t)$ are the two points of intersection for this question?
@user123 It doesn't, $\ln e=1$. The $y$ coordinate is $\ln e$ (same as $1$) when the $x$ coordinate is $e$.
2d
reviewed Edit Can someone explain why $(e,1)$ and $(t, \ln t)$ are the two points of intersection for this question?
2d
revised Can someone explain why $(e,1)$ and $(t, \ln t)$ are the two points of intersection for this question?
improved formatting and inlined image
2d
answered Can someone explain why $(e,1)$ and $(t, \ln t)$ are the two points of intersection for this question?
Feb
11
comment Is $2^{\infty}$ an Indeterminate form
Let us continue this discussion in chat.
Feb
11
comment Is $2^{\infty}$ an Indeterminate form
I agree that the original question and questions about whether or not $f(x)^{g(x)}$ would be related to an indeterminate form. I'm just saying that I think the only reason not to be base-agnostic about arguments of the form in your answer would be if you wanted to prepare someone for L'Hospital's rule. If L'Hospital's rule is not in the picture (as I think we agree), then base $2$ or $3$ is just as safe as base $e$.
Feb
11
comment Is $2^{\infty}$ an Indeterminate form
For your first point, I have some calculus books that start from $e^x$ and some that start from $2^x$, but it may very well be more common to start from $e^x$. For your second point, reverting to $2^x$ is equally "safe" if you replace the natural log with the base-2 log. The reason $e$ and $\ln$ are common in these situations is for the purposes of applying L'Hospital's rule, which is not necessary to argue about whether $f(x)^{g(x)}$ leads to an indeterminate form.
Feb
11
comment Is $2^{\infty}$ an Indeterminate form
I don't understand why passing from the continuous function $2^x$ to the continuous function $e^x$ serves as an explanation.
Feb
11
answered Is $2^{\infty}$ an Indeterminate form
Feb
10
comment References on a game with white and black stones
That paper helps a lot! One thing I want to check is if you're still interested in the game where the starting position has an even number of symbols, because I think the paper doesn't discuss that at all (with Black going first). Either way, there's still more interesting stuff to say about this game, though.
Feb
10
revised Integral of $\vec \nabla f(x)$
added tag
Feb
9
comment How do the roots of “$x^2 + bx + c$” change as $b$ is kept constant and $c$ is changed?
@Michelle, "feeling unintelligent": Unfortunately, things like "exploring in mathematics by making convenience-driven choices" are not emphasized early on. And keep in mind that I'm not a math peer; I'm a math teacher. Also, since your question had little context (this is probably why the question is closed), I had to make a guess at what level to pitch my answer at. (Not to mention that answers are not just for the question asker.) If you just keep on asking questions, you'll keep learning.
Feb
9
comment How do the roots of “$x^2 + bx + c$” change as $b$ is kept constant and $c$ is changed?
@Michelle, sorry about any confusion; I'm happy to answer questions about my answers. If I had just defined $S=\sqrt{|b^2-4c|}$ and $R=-b$, then by the quadratic formula, the roots in the real case would be $(R\pm S)/2$ and the roots in the complex case would be $(R\pm iS)/2$. Only to avoid writing "$/2$" in so many places, and for no other reason, I made the choice to define $r=-b/2$ and $s=(\sqrt{|b^2-4c|})/2$ instead. The $1/2$ comes into the definition of $s$ because I chose it to simplify the algebra that followed.
Feb
9
comment References on a game with white and black stones
I've been working here and there on this since you posted it; there's definitely some interesting patterns, but I don't yet have a complete collection of conjectures. I'll probably give up and post my partial results by the end of another week. Where did you come across this game? Or is it your own invention?
Feb
8
comment How do the roots of “$x^2 + bx + c$” change as $b$ is kept constant and $c$ is changed?
@Michelle Consider similar situations with numbers. $\sqrt{3}=\sqrt{|3|}$, since $3>0$. And $\sqrt{-2}=i\sqrt{2}=i\sqrt{|-2|}$ since $-2<0$. So any square root of a real number is related to the square root of its absolute value, possibly with a factor of $i$. Using this same idea, I figured that introducing $\sqrt{\left|b^2-4ac\right|}$ would help in understanding. To avoid having to write something like $s/2$ all the time, I defined $s$ to be $\frac12\sqrt{\left|b^2-4ac\right|}$. Incidentally, "exploratory algebra" was not a typo. There are many different choices you can make when exploring.
Feb
6
answered What is the name for the point where a non-smooth transition occurs
Feb
6
comment Converting programming logic to mathematical notation
@BugHunterUK, "how to write algorithms in math": as Ian said, pseudocode is fairly common. You can find examples in many papers/books on algorithms in graph theory, for instance. "express solutions to problems in math": Most solutions to problems in math are not algorithms. And when they're close to code, they're often closer to code in a pure functional language than a procedural language.
Feb
6
answered Is there a name for dividing a set into pieces, some of which may be empty?