small typo before jumping into kernels

doc/pub/svm/html/._svm-bs009.html

@@ -140,7 +140,7 @@ Thus, we wish to find a margin \( M \) with \( \hat{w} \) normalized to
 \( \vert\vert \hat{w}\vert\vert =1 \) subject to the condition
 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, p. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, p. 
 $$
 
 All points are thus at a signed distance from the decision boundary defined by the line \( L \). The parameters \( b \) and \( w_1 \) and \( w_2 \) define this line.
@@ -148,18 +148,18 @@ All points are thus at a signed distance from the decision boundary defined by t
 <p>
 We seek thus the largest value \( M \) defined by
 $$
-\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, n, 
+\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, n, 
 $$
 
 or just 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \forall i. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \hspace{0.1cm}\forall i. 
 $$
 
 If we scale the equation so that \( \vert \vert \hat{w}\vert\vert = 1/M \), we have to find the minimum of 
 \( \hat{w}^T\hat{w}=\vert \vert \hat{w}\vert\vert \) (the norm) subject to the condition
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \hspace{0.1cm}\forall i.
 $$
 
 <p>

doc/pub/svm/html/._svm-bs012.html

@@ -156,7 +156,7 @@ $$
 subject to the constraints \( \lambda_i\geq 0 \) and \( \sum_i\lambda_iy_i=0 \). 
 We must in addition satisfy the <a href="https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions" target="_self">Karush-Kuhn-Tucker</a> (KKT) condition
 $$
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \forall i.
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \hspace{0.1cm}\forall i.
 $$
 
 

doc/pub/svm/html/._svm-bs016.html

@@ -139,7 +139,7 @@ $$
 
 subject to 
 $$
-y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \forall i,
+y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \hspace{0.1cm}\forall i,
 $$
 
 with the requirement \( \xi_i\geq 0 \).
@@ -157,7 +157,7 @@ $$
 
 and
 $$
-\lambda_i = C-\gamma_i \forall i.
+\lambda_i = C-\gamma_i \hspace{0.1cm}\forall i.
 $$
 
 Inserting these constraints into the equation for \( {\cal L} \) we obtain the same equation as before
@@ -168,7 +168,7 @@ $$
 but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$. 
 We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
 $$
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \forall i,
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
 $$
 
 $$
@@ -177,7 +177,7 @@ $$
 
 and 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \hspace{0.1cm}\forall i.
 $$
 
 <p>

doc/pub/svm/html/svm-reveal.html

@@ -416,7 +416,7 @@ Thus, we wish to find a margin \( M \) with \( \hat{w} \) normalized to
 
 <p>&nbsp;<br>
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, p. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, p. 
 $$
 <p>&nbsp;<br>
 
@@ -426,14 +426,14 @@ All points are thus at a signed distance from the decision boundary defined by t
 We seek thus the largest value \( M \) defined by
 <p>&nbsp;<br>
 $$
-\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, n, 
+\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, n, 
 $$
 <p>&nbsp;<br>
 
 or just 
 <p>&nbsp;<br>
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \forall i. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \hspace{0.1cm}\forall i. 
 $$
 <p>&nbsp;<br>
 
@@ -441,7 +441,7 @@ If we scale the equation so that \( \vert \vert \hat{w}\vert\vert = 1/M \), we h
 \( \hat{w}^T\hat{w}=\vert \vert \hat{w}\vert\vert \) (the norm) subject to the condition
 <p>&nbsp;<br>
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \hspace{0.1cm}\forall i.
 $$
 <p>&nbsp;<br>
 
@@ -604,7 +604,7 @@ subject to the constraints \( \lambda_i\geq 0 \) and \( \sum_i\lambda_iy_i=0 \).
 We must in addition satisfy the <a href="https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions" target="_blank">Karush-Kuhn-Tucker</a> (KKT) condition
 <p>&nbsp;<br>
 $$
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \forall i.
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \hspace{0.1cm}\forall i.
 $$
 <p>&nbsp;<br>
 
@@ -737,7 +737,7 @@ $$
 subject to 
 <p>&nbsp;<br>
 $$
-y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \forall i,
+y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \hspace{0.1cm}\forall i,
 $$
 <p>&nbsp;<br>
 
@@ -761,7 +761,7 @@ $$
 and
 <p>&nbsp;<br>
 $$
-\lambda_i = C-\gamma_i \forall i.
+\lambda_i = C-\gamma_i \hspace{0.1cm}\forall i.
 $$
 <p>&nbsp;<br>
 
@@ -776,7 +776,7 @@ but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=
 We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
 <p>&nbsp;<br>
 $$
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \forall i,
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
 $$
 <p>&nbsp;<br>
 
@@ -789,7 +789,7 @@ $$
 and 
 <p>&nbsp;<br>
 $$
-y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \hspace{0.1cm}\forall i.
 $$
 <p>&nbsp;<br>
 </section>

doc/pub/svm/html/svm-solarized.html

@@ -328,7 +328,7 @@ Thus, we wish to find a margin \( M \) with \( \hat{w} \) normalized to
 \( \vert\vert \hat{w}\vert\vert =1 \) subject to the condition
 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, p. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, p. 
 $$
 
 All points are thus at a signed distance from the decision boundary defined by the line \( L \). The parameters \( b \) and \( w_1 \) and \( w_2 \) define this line.
@@ -336,18 +336,18 @@ All points are thus at a signed distance from the decision boundary defined by t
 <p>
 We seek thus the largest value \( M \) defined by
 $$
-\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, n, 
+\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, n, 
 $$
 
 or just 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \forall i. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \hspace{0.1cm}\forall i. 
 $$
 
 If we scale the equation so that \( \vert \vert \hat{w}\vert\vert = 1/M \), we have to find the minimum of 
 \( \hat{w}^T\hat{w}=\vert \vert \hat{w}\vert\vert \) (the norm) subject to the condition
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \hspace{0.1cm}\forall i.
 $$
 
 <p>
@@ -476,7 +476,7 @@ $$
 subject to the constraints \( \lambda_i\geq 0 \) and \( \sum_i\lambda_iy_i=0 \). 
 We must in addition satisfy the <a href="https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions" target="_blank">Karush-Kuhn-Tucker</a> (KKT) condition
 $$
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \forall i.
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \hspace{0.1cm}\forall i.
 $$
 
 
@@ -588,7 +588,7 @@ $$
 
 subject to 
 $$
-y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \forall i,
+y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \hspace{0.1cm}\forall i,
 $$
 
 with the requirement \( \xi_i\geq 0 \).
@@ -606,7 +606,7 @@ $$
 
 and
 $$
-\lambda_i = C-\gamma_i \forall i.
+\lambda_i = C-\gamma_i \hspace{0.1cm}\forall i.
 $$
 
 Inserting these constraints into the equation for \( {\cal L} \) we obtain the same equation as before
@@ -617,7 +617,7 @@ $$
 but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$. 
 We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
 $$
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \forall i,
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
 $$
 
 $$
@@ -626,7 +626,7 @@ $$
 
 and 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \hspace{0.1cm}\forall i.
 $$
 
 <p>

doc/pub/svm/html/svm.html

@@ -333,7 +333,7 @@ Thus, we wish to find a margin \( M \) with \( \hat{w} \) normalized to
 \( \vert\vert \hat{w}\vert\vert =1 \) subject to the condition
 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, p. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, p. 
 $$
 
 All points are thus at a signed distance from the decision boundary defined by the line \( L \). The parameters \( b \) and \( w_1 \) and \( w_2 \) define this line.
@@ -341,18 +341,18 @@ All points are thus at a signed distance from the decision boundary defined by t
 <p>
 We seek thus the largest value \( M \) defined by
 $$
-\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, n, 
+\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, n, 
 $$
 
 or just 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \forall i. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \hspace{0.1cm}\forall i. 
 $$
 
 If we scale the equation so that \( \vert \vert \hat{w}\vert\vert = 1/M \), we have to find the minimum of 
 \( \hat{w}^T\hat{w}=\vert \vert \hat{w}\vert\vert \) (the norm) subject to the condition
 $$
-y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \hspace{0.1cm}\forall i.
 $$
 
 <p>
@@ -481,7 +481,7 @@ $$
 subject to the constraints \( \lambda_i\geq 0 \) and \( \sum_i\lambda_iy_i=0 \). 
 We must in addition satisfy the <a href="https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions" target="_blank">Karush-Kuhn-Tucker</a> (KKT) condition
 $$
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \forall i.
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \hspace{0.1cm}\forall i.
 $$
 
 
@@ -593,7 +593,7 @@ $$
 
 subject to 
 $$
-y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \forall i,
+y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \hspace{0.1cm}\forall i,
 $$
 
 with the requirement \( \xi_i\geq 0 \).
@@ -611,7 +611,7 @@ $$
 
 and
 $$
-\lambda_i = C-\gamma_i \forall i.
+\lambda_i = C-\gamma_i \hspace{0.1cm}\forall i.
 $$
 
 Inserting these constraints into the equation for \( {\cal L} \) we obtain the same equation as before
@@ -622,7 +622,7 @@ $$
 but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$. 
 We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
 $$
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \forall i,
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
 $$
 
 $$
@@ -631,7 +631,7 @@ $$
 
 and 
 $$
-y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \hspace{0.1cm}\forall i.
 $$
 
 <p>

doc/pub/svm/ipynb/svm.ipynb

@@ -359,7 +359,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "y_i(\\hat{w}^T\\hat{x}_i+b) \\geq M \\forall i=1,2,\\dots, p.\n",
+    "y_i(\\hat{w}^T\\hat{x}_i+b) \\geq M \\hspace{0.1cm}\\forall i=1,2,\\dots, p.\n",
     "$$"
    ]
   },
@@ -377,7 +377,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\frac{1}{\\vert \\vert \\hat{w}\\vert\\vert}y_i(\\hat{w}^T\\hat{x}_i+b) \\geq M \\forall i=1,2,\\dots, n,\n",
+    "\\frac{1}{\\vert \\vert \\hat{w}\\vert\\vert}y_i(\\hat{w}^T\\hat{x}_i+b) \\geq M \\hspace{0.1cm}\\forall i=1,2,\\dots, n,\n",
     "$$"
    ]
   },
@@ -393,7 +393,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "y_i(\\hat{w}^T\\hat{x}_i+b) \\geq M\\vert \\vert \\hat{w}\\vert\\vert \\forall i.\n",
+    "y_i(\\hat{w}^T\\hat{x}_i+b) \\geq M\\vert \\vert \\hat{w}\\vert\\vert \\hspace{0.1cm}\\forall i.\n",
     "$$"
    ]
   },
@@ -410,7 +410,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "y_i(\\hat{w}^T\\hat{x}_i+b) \\geq 1 \\forall i.\n",
+    "y_i(\\hat{w}^T\\hat{x}_i+b) \\geq 1 \\hspace{0.1cm}\\forall i.\n",
     "$$"
    ]
   },
@@ -711,7 +711,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\lambda_i\\left[y_i(\\hat{w}^T\\hat{x}_i+b) -1\\right] \\forall i.\n",
+    "\\lambda_i\\left[y_i(\\hat{w}^T\\hat{x}_i+b) -1\\right] \\hspace{0.1cm}\\forall i.\n",
     "$$"
    ]
   },
@@ -914,7 +914,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "y_i(\\hat{w}^T\\hat{x}_i+b)=1-\\xi_i \\forall i,\n",
+    "y_i(\\hat{w}^T\\hat{x}_i+b)=1-\\xi_i \\hspace{0.1cm}\\forall i,\n",
     "$$"
    ]
   },
@@ -964,7 +964,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\lambda_i = C-\\gamma_i \\forall i.\n",
+    "\\lambda_i = C-\\gamma_i \\hspace{0.1cm}\\forall i.\n",
     "$$"
    ]
   },
@@ -1037,7 +1037,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "y_i(\\hat{w}^T\\hat{x}_i+b) -(1-\\xi_) \\geq 0 \\forall i.\n",
+    "y_i(\\hat{w}^T\\hat{x}_i+b) -(1-\\xi_) \\geq 0 \\hspace{0.1cm}\\forall i.\n",
     "$$"
    ]
   },

doc/src/SupportVMachines/svm.do.txt

@@ -215,7 +215,7 @@ $\vert\vert \hat{w}\vert\vert =1$ subject to the condition
 
 !bt
 \[
-y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, p. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, p. 
 \]
 !et
 All points are thus at a signed distance from the decision boundary defined by the line $L$. The parameters $b$ and $w_1$ and $w_2$ define this line. 
@@ -223,20 +223,20 @@ All points are thus at a signed distance from the decision boundary defined by t
 We seek thus the largest value $M$ defined by
 !bt
 \[
-\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \forall i=1,2,\dots, n, 
+\frac{1}{\vert \vert \hat{w}\vert\vert}y_i(\hat{w}^T\hat{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, n, 
 \]
 !et
 or just 
 !bt
 \[
-y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \forall i. 
+y_i(\hat{w}^T\hat{x}_i+b) \geq M\vert \vert \hat{w}\vert\vert \hspace{0.1cm}\forall i. 
 \]
 !et
 If we scale the equation so that $\vert \vert \hat{w}\vert\vert = 1/M$, we have to find the minimum of 
 $\hat{w}^T\hat{w}=\vert \vert \hat{w}\vert\vert$ (the norm) subject to the condition
 !bt
 \[
-y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) \geq 1 \hspace{0.1cm}\forall i.
 \]
 !et
 
@@ -373,7 +373,7 @@ subject to the constraints $\lambda_i\geq 0$ and $\sum_i\lambda_iy_i=0$.
 We must in addition satisfy the "Karush-Kuhn-Tucker":"https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions" (KKT) condition
 !bt
 \[
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \forall i.
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -1\right] \hspace{0.1cm}\forall i.
 \]
 !et
 o If $\lambda_i > 0$, then $y_i(\hat{w}^T\hat{x}_i+b)=1$ and we say that $x_i$ is on the boundary.
@@ -478,7 +478,7 @@ This has in turn the consequences that we change our optmization problem to find
 subject to 
 !bt
 \[
-y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \forall i,
+y_i(\hat{w}^T\hat{x}_i+b)=1-\xi_i \hspace{0.1cm}\forall i,
 \]
 !et
 with the requirement $\xi_i\geq 0$.
@@ -498,7 +498,7 @@ and
 and
 !bt
 \[
-\lambda_i = C-\gamma_i \forall i.
+\lambda_i = C-\gamma_i \hspace{0.1cm}\forall i.
 \]
 !et
 Inserting these constraints into the equation for ${\cal L}$ we obtain the same equation as before
@@ -511,7 +511,7 @@ but now subject to the constraints $\lambda_i\geq 0$, $\sum_i\lambda_iy_i=0$ and
 We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
 !bt
 \[
-\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \forall i,
+\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
 \]
 !et
 !bt
@@ -522,7 +522,7 @@ We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
 and 
 !bt
 \[
-y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \forall i.
+y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_) \geq 0 \hspace{0.1cm}\forall i.
 \]
 !et