Difference between revisions of "User:Temperal/The Problem Solver's Resource Competition"

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<cmath>
 
<cmath>
 
\begin{align*}
 
\begin{align*}
     |\langle (z,i), (i,w)\rangle| &\leq ||(z,i)||||(i,w)|| \\
+
     |\langle (z,-i), (i,\overline{w})\rangle| &\leq ||(z,i)||||(i,w)|| \\
     |iz + iw|^2 &\leq (|z|^2 + 1)(|w|^2 + 1) \\
+
     |-iz - i\overline{w}|^2 &\leq (|z|^2 + 1)(|w|^2 + 1) \\
     \frac{|z + w|^2}{|z|^2 + 1} &\leq |w|^2 + 1
+
     \frac{|z + \overline{w}|^2}{|z|^2 + 1} &\leq |w|^2 + 1
 
\end{align*}|
 
\end{align*}|
 
</cmath>
 
</cmath>

Revision as of 13:41, 8 October 2024

\begin{align*}     |\langle (z,-i), (i,\overline{w})\rangle| &\leq ||(z,i)||||(i,w)|| \\     |-iz - i\overline{w}|^2 &\leq (|z|^2 + 1)(|w|^2 + 1) \\     \frac{|z + \overline{w}|^2}{|z|^2 + 1} &\leq |w|^2 + 1 \end{align*}|