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A group of fine and pure mathématique. Available in crystal and freebase form.
Cause you may be given an interesting operation(not the standard addition or multiplication), and so might have to show closure
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Definition of Group. Notice that they haven't used closure as one of its axiom because they have already mentioned binary operation. So no need to use closure as one of its axiom.
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Every definition of a group in abstract algebra books that I have come across mentions closure as one of its axioms.
However, if you have already specified that the operation is a binary operation on (G), then there is no need to list closure separately as an axiom, because a binary operation on (G) is, by definition, closed.
LOL, my account wasn’t working as it should. Someone or some bot might have hacked into it. Everything is fine now, though. Sorry for the inconvenience!
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https://youtu.be/NBB8D8Pr1Ss?si=l1JYD29puUVmmZ2C
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Yeah, I don't like your flooding. R has been muted.
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https://youtube.com/shorts/z_CUGl_GYwg?si=qVF-oZU7USd82nSr
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Thank you
By now @tuz_ar will remember that here we are not answer machine.
You're right. But when told to show that a given set is actually a group, at least from my coursework, we were required to show that
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As we all know
12 sides in a cube
...............
Size of one side of small cube = 2 m
Perimeter of smaller one = 12×2 = 24 m
...............
Size of one side of bigger one cube = 4m
Perimeter of bigger one = 12×4 = 48 m
................
Hence perimeter of both = 24+48 = 64 m
................
................
If options contain 62 m
Then according to figure
62 will be correct
https://youtu.be/vrDK9cfLK7Q?si=n09hVZmC77iCdV0E
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https://youtu.be/TCyMfqhczcE?si=liG9Y4U3U1_hMlq8
Check it out 👍
https://youtu.be/cahZ5PBsAfU
Introduction to the Abstract Algebra Series
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