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comment Can a real continuous bounded function on $ \Bbb{R}^{2} $ be expressed as a finite sum of products of real continuous functions on $ \Bbb{R} $?
Fair enough. In some ways $e^{xy}$ is a nicer example! but the OP wanted a bounded function for some reason.
Apr
25
answered Can a real continuous bounded function on $ \Bbb{R}^{2} $ be expressed as a finite sum of products of real continuous functions on $ \Bbb{R} $?
Apr
24
comment Closed form for Numbers in a Triangular Array
Have you tried generating functions?
Apr
22
answered What does a polynomial look like under projection of underlying space?
Apr
22
answered What is the relationship between the trigonometric secant and the geometric secant of a circle?
Apr
22
comment Equality by iteratively applying $(a,b)\rightarrow [(a+1,2b)\text{ or }(2a,b+1)]$?
I think the combination of the two tags is pretty accurate.
Apr
22
comment Series for $\sin(z) / \sin(\pi z)$
Why do you think the identity is true?
Apr
21
revised Two pawns walking in a complete graph
deleted 1 character in body
Apr
21
comment Translating English to symbolic logic
I think this translation of my statement is more accurate: "For each student, there is a teacher whom that student sent a letter to." (Your attempt doesn't accurately capture the fact that the student referred to in the first half and the student referred to in the second half must be the same student.)
Apr
21
comment Translating English to symbolic logic
You can use any letters you want for the arguments of $P$ and $T$. For (c), I would use $\forall x \big( P(x) \implies \exists y ( T(y) \land E(x,y) ) \big)$. Your attempt, $\forall x \exists y \big( P(x) \land T(y) \implies E(x,y) \big)$, would be true for instance if there just exists a single non-teacher $y$, regardless of any letter-sending.
Apr
20
comment Small proximity of important points of a function
Yep. But since you didn't indicate any thoughts or partial progress whatsoever in your question, I decided to take a little time and write something that might help. If you have already done some work and don't want people to repeat it, you should say so in detail in the original post.
Apr
20
comment Show that f and e^f can not have a common pole
typo fixed - the image contains a small disc centered at $0$, not $x_0$
Apr
20
revised Show that f and e^f can not have a common pole
deleted 2 characters in body
Apr
20
comment Small proximity of important points of a function
Well, $s$ is the root of $a^x+b^x=c^x$, while $r$ is the root of $a^x\ln a+b^x\ln b=c^x\ln c$. And $b>\frac c2$ by your inequalities, so $\ln b$ isn't too far from $\ln c$ - maybe you can get some mileage out of that....
Apr
19
revised Small proximity of important points of a function
edited tags
Apr
19
comment Small proximity of important points of a function
You should assume that $c>\max\{a,b\}$, or otherwise $f(x)$ tends to infinity. Also, is it important that $a,b,c$ are integers?
Apr
18
comment Asymptotic behavior a recursion involving min/max
Have you computed enough terms to make an educated guess?
Apr
18
answered What would the expected number of swaps in a merge sort be?
Apr
18
answered Calculating the expected value of a random variable that's a function of a random variable
Apr
17
comment Sum of digits of $11\dots 11^2$ where $11\dots 11$ is a 1992 digit number with all digits $1$
What is the proof that the average digit value will be $4.5$? It certainly doesn't happen for small values of $n$; what property of $n$ implies this, and why?