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Jun
8
comment What are some results that shook the foundations of one or more fields of mathematics?
I understand the question may have many possible answers, but I think it is sufficiently narrow that we can distinguish an answer from a non-answer in general, no?
Jun
8
comment True or False. $K_{2n}$ ( complete graph with 2n vertices) has Euler circuit.
@BrianTung for n=1 it's K_2
Jun
8
comment True or False. $K_{2n}$ ( complete graph with 2n vertices) has Euler circuit.
n=1 is an obvious counterexample
Feb
18
comment Given a vector $x\in \mathbb R^n$, how can we find $z\in \mathbb Z^n$ which is closest to a scalar multiple of $x$?
@ThomasAndrews yes that's right
Feb
10
comment Is closed unit disk in $R^2$ be a vector space ?
@RobertIsrael what if we consider the open unit disc?
Feb
9
comment What kind of algorithm might solve this type of optimization problem?
Very nice. I like to think I would have eventually made the observation about the sum of the terms, but thank you very much for being smarter than me.
Jun
18
comment Contraposition and law of excluded middle
@Materialist as far as I know (I am not an expert), the law of the excluded middle is formally equivalent to negation elimination. If we can obtain a statement without using negation elimination (i.e. without invoking $\neg\neg P \iff P$), we have proven it without making use of the law of the excluded middle. Here, we begin with, say, $(A\to B) \& \neg B$. If we can now show $\neg A$, then we've shown that $(A\to B)\to (B\to A)$. Now, assume $A$; we show that this leads to $B\&\neg B$, which allows us to conclude $\neg A$ without making use of the law of the excluded middle.
Jun
18
comment Extended Monte Hall problem (Hallway)
We start with $n$ doors, and each door has $n$ doors behind it? The answer will be the same—you're not really changing the problem very much; you're just jiggling some parameters around a little bit. Now not switching wins when you select the right door and then select the right door, which happens with probability $1/n^2$. Switching wins when you select the wrong door, change to the right door, and then select the right second door, which happens with probability $\frac{(n-1)}{n}\times\frac{1}{n-1}\times\frac{1}{n}>1/n^2$. Have I interpreted your question correctly?
Jun
2
comment What does “radical cube zero” mean?
For what it's worth, in mathematics, a "dimension" is not something that one can "enter". The dimension of a (vector) space is (roughly) the number of coordinates that it takes to fully specify a point in that space. So whatever references you've found to radical cubes (and I don't know what a radical cube is), it is doubtful that it has anything to do with entering or exiting other dimensions.
Jun
2
comment solve the equation for x
Hello, I've changed your statement of the problem to LaTeX code, which I would recommend learning to get the most out of this site. Can you check to make sure that I've translated correctly?
Apr
15
comment Proof by contradiction and order of statements
@Amateur yep. I take it back.
Apr
15
comment Proof by contradiction and order of statements
@Amateur I'm not sure that it's correct to say that $\mathbb{R}$ is a closed interval, although you're certainly right that it's a closed set.
Apr
15
comment Proof by contradiction and order of statements
For your last note, just make a truth table and check.
Apr
15
comment applications of derivatives : maxima and minima
Do you have any thoughts on this? What would it mean if the derivative of a function at a point was $10100$? What would the function look like at that point? Why couldn't that be a maximum?
Apr
15
comment Problem with trigonometric equation
That problem looks pretty tough to solve analytically to me. Where did you come across it?
Apr
15
comment Question about the Continuum Hypothesis
The answer to "where did I go wrong" is that OP took "Clearly this is either true or false - there either exists such a set, or there does not exist such a set" to be true, and this demonstrates that that's not so obvious.
Apr
14
comment If $x^2 +xy =10$ then when $x=2$ what is $\frac{\mathrm dy}{\mathrm dx}$?
do you mean "when $x=2$"?
Apr
14
comment Probability Equation That I am missing here
"Don't ask me why but I just logically see that it is 50% so why?" That's a dangerous way to think about math.
Apr
13
comment Writing Series as a Telescoping Series
yes, I was mistaken, sorry :(. I realized immediately and deleted my comment.
Apr
13
comment Proof by induction valid or not?
@DavidK I know. But either way, it is never correct to assume that the formula works for all $n$.