安裝中文字典英文字典辭典工具!
安裝中文字典英文字典辭典工具!
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- functions - What does y=y (x) mean? - Mathematics Stack Exchange
In many diciplines that utlizes mathematics, we often see the equation $$y=y(x)$$ where $y$ might be other replaced by whichever letter that makes the most sense in
- Let G be a group such that $ (xy)^2 = (yx)^2$ for all x, y ∈ G. Show . . .
0 This might be same argument as in previous answer: $$ (x^ {-1}\cdot yx)^2= (yx\cdot x^ {-1})^2 \,\,\,\, \Rightarrow \,\,\,\, x^ {-1}y^2x=y^2 $$
- If $xy=yx$ in group $G$, then $ (xy)^n=x^ny^n$ [duplicate]
I am showing that if for some group $G$, $xy=yx$ for every $x, y \in G$ then $$ (xy)^n=x^ny^n $$ I claim this holds by induction on $n$ So base case if $n=1$, we
- $x^y = y^x$ for integers $x$ and $y$ - Mathematics Stack Exchange
We know that $2^4 = 4^2$ and $(-2)^{-4} = (-4)^{-2}$ Is there another pair of integers $x, y$ ($x\\neq y$) which satisfies the equality $x^y = y^x$?
- The relationship between the eigenvalues of matrices $XY$ and $YX$
3 You could modify the proof of Sylvester's determinant theorem to show that $$\text {det} \left ( \lambda I_m - XY \right) = \text {det} \left ( \lambda I_n - YX \right)$$ for all $\lambda \neq 0$ This shows equivalence for all nonzero eigenvalues For the zero eigenvalues, an application of the fundamental theorem of algebra is sufficient
- calculus - Finding $y$ by implicit differentiation if $x^y=y^x . . .
Both your expressions are the same :) It is just multiplying by (-1) in the numerator and denominator
- When does $xxyy = xyxy$ not imply $xy = yx$ in a ring?
One thought I had is that "whenever $x^ {-1},y^ {-1}$ exist in $R$, then $xxyy=xyxy\implies xy=yx$"
- number theory - Unspecified $x^y$ vs. $y^x$ - which is larger . . .
This problem is completely symmetric in $x$ and $y$ - how would we be able to tell which one is larger? If $x^y>y^x$, then we can simply swap $x$ and $y$ to obtain a
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