Commit: 6e94336a - lawrd hav mercy
Author: lhorva <lhorva@student.ethz.ch>
Date: 2026-01-13T03:14:39+01:00
Changes: 19 note(s) changed (0 added, 19 modified, 0 deleted)
ℹ️ Cosmetic Changes Hidden: 3 note(s) had formatting-only changes and are not shown below • 2 HTML formatting changes • 1 mixed cosmetic changes
D2>~h
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| Text | The ADT <b>quue</b> has the following operations:<br><ul><li><b>enqueue(k, S)</b>: {{c2:: append at the end of the queue}}</li><li><b>dequeue(S)</b>: {{c4:: remove and return the first element of the queue}}</li></ul> | The ADT <b>queue</b> has the following operations:<br><ul><li><b>enqueue(k, S)</b>: {{c2:: append at the end of the queue}}</li><li><b>dequeue(S)</b>: {{c4:: remove and return the first element of the queue}}</li></ul> |
o3QNr=]FF`
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| Back | We contract \(\{v, w\}\) by:<br><ol><li> |
We contract \(\{v, w\}\) by:<br><ol><li>Replacing \(v\) and \(w\) by a single vertex \(vw\)</li><li>Replacing any edge \(\{v,x\}\) or \(\{w, x\}\) by \(\{vw, x\}\).</li><li>Set the weights to their previous ones, and the minimum if there was more than one.</li></ol> |
fDaa%yb|#1
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| Text | A proof system is {{c2:: |
A proof system is {{c2::<b>complete</b>}} if {{c1:: every true statement has a proof: \(\phi(s, p) = 1 \Longleftarrow \tau(s) = 1\)}}. |
ui6=/w5,Pi
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| Text | An element \(p \in \mathcal{P}\) is either a valid proof for a statement \(s \in \mathcal{S}\) or it's not. |
An element \(p \in \mathcal{P}\) is either a valid proof for a statement \(s \in \mathcal{S}\) or it's not. This is defined by the {{c1::<b>verification function</b> \(\phi : \mathcal{S} \times \mathcal{P} \rightarrow \{0, 1\}\)}}. |
wJPBh5aLN<
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| Text | \(F[x]^*_{(m(x))}\) is {{c1:: a field}} |
\(F[x]^*_{(m(x))}\) is {{c1:: a field.::which type of algebra?}} |
Ap->IRX#;C
If "obj = null" then "obj instanceof String" returns false (never an exception)If "obj = null" then "obj instanceof String" returns false (never an exception)If "String obj = null" then "obj instanceof String" returns false (never an exception).If "String obj = null" then "obj instanceof String" returns false (never an exception).| Field | Before | After |
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| Text | <div><code><span style="font-family: "Liberation Sans";">If "</span>obj = null"</code> then "<code>obj instanceof String"</code> returns {{c1::false (never an exception)}}</div> | <div><code><span style="font-family: "Liberation Sans";">If "String </span>obj = null"</code> then "<code>obj instanceof String"</code> returns {{c1::false (never an exception)}}.</div> |
G#$#7KW!b}
instanceof never throws an exception, just compile errors.instanceof never throws an exception, just compile errors.| Field | Before | After |
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| Front | instanceof can result in a Compile / Runtime / No error? |
LHfofYY0cF
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| Front | Can we us |
Can we use <b>++</b> and <b>--</b> on floats and doubles? |
AG3+NsB]T%
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| Text | \(\mathbb{R}^{m \times n}\) is not actually a new vector space, it is isomorphic to {{c1::\(\mathbb{R}^{m \cdot n}\)}} | \(\mathbb{R}^{m \times n}\) is not actually a new vector space, it is isomorphic to {{c1::\(\mathbb{R}^{m \cdot n}\)}}. |
LIjab7I=97
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| Text | <div>Let \(V\) be a vector space. A nonempty set \(U \subseteq V\) is called a subspace of \(V\) if the following two axioms of a subspace are true for all \(v, w \in U\) and all \(\lambda \in \mathbb{R}\):</div><div><ul><li>{{ |
<div>Let \(V\) be a vector space. A nonempty set \(U \subseteq V\) is called a subspace of \(V\) if the following two axioms of a subspace are true for all \(v, w \in U\) and all \(\lambda \in \mathbb{R}\):</div><div><ul><li>{{c2::\(v + w \in U\) (closure addition)}}</li><li>{{c3::\(\lambda v \in U\) (closure multiplication)}}</li></ul></div><blockquote><ul> </ul></blockquote> |
glVCl00~J+
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| Text | The {{c1:: |
The {{c1::column space, row space and nullspaces (left and right)::fundamental subspaces}} are subspaces of \(\mathbb{R}^m\)/\(\mathbb{R}^n\). |
iwDw^,XMof
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| Text | For any two arbitrary subspaces \(U, W \) of \(V\), we have {{c1:: |
For any two arbitrary subspaces \(U, W \) of \(V\), we have {{c1::\(\{0\}\)}} \(\subseteq U \cap W\). |
jGly4b:5@T
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| Text | <div>Let \(T :V \rightarrow W\) be a bijective linear transformation between vector spaces \(V\) and \(W\) . Let \(B = {v1, v2, . . . , v_l} \subseteq V\) be a finite set of size \(l\), and let \[ T(B) = {T(v_1), T(v_2), \dots, T(v_l)} \subseteq Q \] be the transformed set.</div><div><br></div><div>Then {{c1::\(|T(B)| = |B|\):: |
<div>Let \(T :V \rightarrow W\) be a bijective linear transformation between vector spaces \(V\) and \(W\) . Let \(B = {v1, v2, . . . , v_l} \subseteq V\) be a finite set of size \(l\), and let \[ T(B) = {T(v_1), T(v_2), \dots, T(v_l)} \subseteq Q \] be the transformed set.</div><div><br></div><div>Then {{c1::\(|T(B)| = |B|\)::cardinality comparison}}. Moreover, \(B\) is a basis of \(V\) if and only if {{c1::\(T(B)\) is a basis of \(W\)}}. We therefore also have {{c1::\(\dim(V) = \dim(W)\)}}.</div> |
p>awtIqE5t
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| Text | Let \(V\) be a finitely generated vector space.<br>Then {{c2::\(\dim(V)\) the dimension of \(V\)}} is {{c1::the size of an arbitrary basis \(B\) of \(V\)}}. | Let \(V\) be a finitely generated vector space.<br><br>Then {{c2::\(\dim(V)\) the dimension of \(V\)}} is {{c1::the size of an arbitrary basis \(B\) of \(V\)::given by which basis property?}}. |
v>PZpE,mn~
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| Text | <div>Let \(V\) be a finitely generated vector space, \(F \subseteq V\) a finite set of linearly independent vectors (note that \(F\) does not need to span \(V\)) and \(G \subseteq V\) a finite set of vectors with \(\textbf{Span}(G) = V\) (but they |
<div>Let \(V\) be a finitely generated vector space, \(F \subseteq V\) a finite set of linearly independent vectors (note that \(F\) does not need to span \(V\)) and \(G \subseteq V\) a finite set of vectors with \(\textbf{Span}(G) = V\) (but they don't all need to be independent). Then the following two statements hold:</div><div><ol><li>{{c1::\(|F| \leq |G|\)}}</li><li>{{c2::There exists a subset \(E \subseteq G\) of size \(|G| - |F|\) such that \(\textbf{Span}(F \cup E) = V\).}}</li></ol></div><blockquote><ol> </ol></blockquote> |
xs#S^-Mehy
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| Text | \(\det A^{-1} =\) {{c1::\((\det |
\(\det (A^{-1}) =\) {{c1::\((\det (A))^{-1}\)}} |