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I just realized that there are an infinite number of algebras and an infinite number of abstractions of those algebras.
You can have a group, a group of groups, and a group of group of groups.
When does the madness end? Can you create a ring of rings? Or a ring of groups? Or what about a group of rings?
So long as there are commonalities between them it is possible?
Help me /sci/
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>>8380326
>group of groups
?
under what operation does this work?
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>>8380364
I have no idea, but theres gotta be a way to transfer between groups some how.
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>>8380372
i dont think so bud
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>>8380326
>When does the madness end?
The monster group.
>not really but it should
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>>8380378
though i guess you could maybe define a monoid of groups using direct product?
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>>8380364
If we're talking about a finite set of [math]n[/math] groups, you can easily construct [math]n![/math] different groups homomorphic to [math]\mathbb{Z}_n[/math] :^).
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>>8380434
>trivial arrangements of group tables
highly non-interesting anon
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>>8380379
I would fuck her monster group if you know what I'm saying hahah!!!
That said, it is funny how that girl is waving her hair and doing 'hair art' or some shit when I and everyone who saw that webm just looked at her ass. Yeah, admit it. YOU looked at her ass every single second.
Why do girls in 2016 still pretend like people care about other shit? Like Jessica Nigri doing cosplay. Bitch, we are looking at your tits. You could cosplay a character that DOESN'T EXIST and we wouldn't notice.
Fucking cosplay Mulinlinlong Futon from Disney's Molongulan.
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>>8380364
Do the trig functions make a group?
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>>8380558
you need to give an operation for a group bud, not just a set
come up with a group operation for the set of trig functions then get back to me and i'll let you know if they're a group
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>>8380570
I have no idea really, what about some series of trig functions? Adding a bunch of different ones?
Is that the fourier series? Is that a group.
Like I said, im pretty new to this math stuff.
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>>8380800
sums of sines form fourier series, and the fourier series is a vector space, which means it's also a group.
Groups are boring anyway, rings are where it's at.
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>>8380806
Rings suck. Fields are where its at. Enjoy your shitty and few operations
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>>8380835
Field is a commutative ring where each non-zero element is reversible.
Dunno
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>>8380835
fields are rings where every element has an inverse.
polynomials and integers form a ring under the obvious operations
rationals, reals, and complex numbers are fields.
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>>8380844
every non-zero element bud
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>>8380844
Commutativity also. Without commutativity it's a division ring
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>>8380570
maybe the derivative operation?
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>>8382115
The group operation is binary.
Thread posts: 21
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Thread images: 8