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Title: Cancellation Property
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Series: Algebra
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YouTube-Title: Algebra 6 | Cancellation Property
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Bright video: https://youtu.be/Ncifg6nmu8U
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Dark video: https://youtu.be/seiG04U6EEM
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Ad-free video: Watch Vimeo video
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Quiz: Test your knowledge
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Dark-PDF: Download PDF version of the dark video
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Print-PDF: Download printable PDF version
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Thumbnail (bright): Download PNG
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Thumbnail (dark): Download PNG
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Subtitle on GitHub: alg06_sub_eng.srt missing
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Definitions in the video: order of a group, order of a semigroup
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: What is the order of the group $G = (\mathbb{R}, +)$, written as $\mathrm{ord}(G)$?
A1: $1$
A2: $2$
A3: $\infty$
A4: $n$
Q2: What is the order of the group $G = ({ e,a }, \circ) $ where $a \circ a = e$.
A1: $1$
A2: $2$
A3: $\infty$
A4: $n$
Q3: Let $(S, \circ)$ be a semigroup. What is the statement of the right-cancellation property?
A1: If $x b = y b$, then $x = y$.
A2: If $x b = y a$, then $x = y$.
A3: If $b x = y a$, then $x = y$.
A4: If $b x = b y$, then $x = y$.
Q4: Let $(S, \circ)$ be a semigroup given by the following sets of matrices together with the matrix multiplication: $$ \left{ \begin{pmatrix} a & b \ 0 & 0 \end{pmatrix} \biggm| a,b \in \mathbb{R} \right} $$ Do we have the right-cancellation property here?
A1: No, we find counterexamples!
A2: Yes!
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Last update: 2024-11
