query: If $y^y=x$, can $y$ be expressed as a function of $x$?
positive_passages.docid: 24307
positive_passages.text: Is $x^x=y$ solvable for $x$?
negative_passages.docid: 153355
negative_passages.text: Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?
negative_passages.docid: 158551
negative_passages.text: If $X \perp Y$ and $X+Y \in L^1$ then $X,Y \in L^1$
negative_passages.docid: 22303
negative_passages.text: How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
negative_passages.docid: 65371
negative_passages.text: Does $2^X \cong 2^Y$ imply $X \cong Y$ without assuming the axiom of choice?
negative_passages.docid: 21891
negative_passages.text: If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
negative_passages.docid: 121353
negative_passages.text: If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
negative_passages.docid: 156536
negative_passages.text: Defining functions as derivatives
negative_passages.docid: 45319
negative_passages.text: Properties of $y$ if $\frac{d^2y}{dx^2}+xy=0$, $x \in [a,b],$ and $y(a)=y(b)=0.$
negative_passages.docid: 157733
negative_passages.text: Are positive real numbers $x,y$ allowed to be taken out during this proof?
negative_passages.docid: 33332
negative_passages.text: A classic exponential inequality: $x^y+y^x>1$
negative_passages.docid: 134880
negative_passages.text: Is there a difference between $y(x)$ and $f(x)$
negative_passages.docid: 125788
negative_passages.text: A function with a property $f(x+y)=f(x)f(y)$
negative_passages.docid: 22821
negative_passages.text: May $y=e^x$ be satisfied with both $x$ and $y$ $\in$ $\mathbb{Z}^+$?
negative_passages.docid: 25953
negative_passages.text: Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
negative_passages.docid: 31846
negative_passages.text: Does $\neg(x > y)$ imply that $y \geq x$?
negative_passages.docid: 65319
negative_passages.text: For all $x,y∈\Bbb{R}$ define that $ x\equiv y$ if$ x^2=y^2$