/sci/ - Science & Math » Thread #14101949

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Anonymous Fri 14 Jan 15:13:53 2022 No.14101949 View Reply Original Report

Quoted By: >>14102344 >>14102685 >>14102802

The complement of the union of two sets is equal to the intersection of their complements and the complement of the intersection of two sets is equal to the union of their complements

Anonymous

Anonymous Fri 14 Jan 2022 15:57:42 No.14102082 Report

Quoted By: >>14102089 >>14102745

But what is a "set"?

Anonymous

Anonymous Fri 14 Jan 2022 15:59:42 No.14102089 Report

Quoted By: >>14102179

>>14102082
a collection of things
simple as

Anonymous

Anonymous Fri 14 Jan 2022 16:23:57 No.14102179 Report

Quoted By: >>14102187

>>14102089
The collection of all trivial groups is not a set though.

Anonymous

Anonymous Fri 14 Jan 2022 16:26:02 No.14102187 Report

Quoted By: >>14102375

>>14102179
why

Anonymous

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Anonymous Fri 14 Jan 2022 17:06:47 No.14102344 Report

Quoted By: >>14102362

>>14101949
The image of the union of two sets equals the union of their images
The image of the intersection of two sets IS A SUBSET OF the intersection of their images
The inverse image of the union of two sets equals the union of their inverse images
The inverse image of the intersection of two sets equals the intersection of their inverse images
Why is the second one poorly behaved?
CAPTCHA: W0X0K

Anonymous

Anonymous Fri 14 Jan 2022 17:10:09 No.14102362 Report

Quoted By: >>14102373 >>14102657

>>14102344
Let me test out \LaTeX. Let $f : X \to Y$ be a function and $A, B \subseteq X$.
$$f(A \cup B) = f(A) \cup f(B)$$
$$f(A \cap B) \subseteq f(A) \cap f(B)$$
$$f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$$
$$f^{-1}(A \cap B) = f^{-1}(A) \cap f^{-1}(B)$$

Anonymous

Anonymous Fri 14 Jan 2022 17:10:34 No.14102364 Report

Quoted By:

IT'S PAYNE WHACK HIM

Anonymous

Anonymous Fri 14 Jan 2022 17:12:47 No.14102373 Report

Quoted By: >>14102690

>>14102362
$\LaTeX$ attempt #2. Let $f : X \to Y$ be a function and $A, B \subseteq X$ .
$f(A \cup B) = f(A) \cup f(B)$
$f(A \cap B) \subseteq f(A) \cap f(B)$
$f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)$
$f^{-1}(A \cap B) = f^{-1}(A) \cap f^{-1}(B)$

Anonymous

Anonymous Fri 14 Jan 2022 17:12:57 No.14102375 Report

Quoted By: >>14102628

>>14102187
A contemporary mathematician would tell you that it's because it violates some axiom. But he won't tell you why does he consider this axiom to be meaningful when it violates his idea that a set is the same thing as a collection of objects.

Anonymous

Anonymous Fri 14 Jan 2022 18:11:06 No.14102628 Report

Quoted By: >>14102671

>>14102375
which axiom is it

Anonymous

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Anonymous Fri 14 Jan 2022 18:16:56 No.14102657 Report

Quoted By: >>14102708

>>14102362
>He uses double dollar for display math instead of \[ \]

Anonymous

Anonymous Fri 14 Jan 2022 18:18:31 No.14102665 Report

Quoted By: >>14102672

your brain is the set {Ø}

Anonymous

Anonymous Fri 14 Jan 2022 18:19:19 No.14102671 Report

Quoted By: >>14102718

>>14102628
axiom of regularity

Anonymous

Anonymous Fri 14 Jan 2022 18:19:19 No.14102672 Report

Quoted By: >>14102677

>>14102665
so it's not empty

Anonymous

Anonymous Fri 14 Jan 2022 18:20:17 No.14102677 Report

Quoted By:

>>14102672
got him

Anonymous

Anonymous Fri 14 Jan 2022 18:21:18 No.14102685 Report

Quoted By: >>14102694 >>14102706

>>14101949
gibberish just like

>if you combine the two-element set {1,2} with the two-element set {2,3} you get the three-element set {1,2,3}
Set theory is categorically retarded

Anonymous

Anonymous Fri 14 Jan 2022 18:22:34 No.14102690 Report

Quoted By: >>14102711

>>14102373
>violates latex this bad
>still posts it
shame on you

Anonymous

Anonymous Fri 14 Jan 2022 18:23:05 No.14102694 Report

Quoted By: >>14102698 >>14102719

>>14102685
you are mentally ill, seek help

Anonymous

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Anonymous Fri 14 Jan 2022 18:24:23 No.14102698 Report

Quoted By: >>14102724

>>14102694

Anonymous

Anonymous Fri 14 Jan 2022 18:25:04 No.14102706 Report

Quoted By: >>14102728

>>14102685
You're quoting the axiom of union. What else would the union of {1,2} and {2,3} be?

Anonymous

Anonymous Fri 14 Jan 2022 18:25:53 No.14102708 Report

Quoted By: >>14102732

>>14102657
Why should I use \[ \]?

Anonymous

Anonymous Fri 14 Jan 2022 18:26:53 No.14102711 Report

Quoted By:

>>14102690
What did I do wrong? I'm a first-year in university have mercy on me.

Anonymous

Anonymous Fri 14 Jan 2022 18:28:17 No.14102718 Report

Quoted By: >>14102756

>>14102671
i googled it and I still don't get it

Anonymous

Anonymous Fri 14 Jan 2022 18:28:17 No.14102719 Report

Quoted By:

>>14102694
>mentally ill
>implying a metric with respect to the mind
>prob believes in ADHD and alcoholism
zoomer

Anonymous

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Anonymous Fri 14 Jan 2022 18:29:10 No.14102724 Report

Quoted By:

>>14102698
wrong picture lmao

Anonymous

Anonymous Fri 14 Jan 2022 18:29:40 No.14102728 Report

Quoted By: >>14102743

>>14102706
a four element set

Anonymous

Anonymous Fri 14 Jan 2022 18:30:41 No.14102732 Report

Quoted By: >>14102835

>>14102708
$$ is TeX syntax and not officially supported by LaTeX, and it can't be redefined. Spacing is off, some LaTeX syntax doesn't work inside a $$ environment.

\[ is redefineable and is by default \begin{displaymath}. It's LaTeX syntax and works out of the box with other LaTeX syntax.

Anonymous

Anonymous Fri 14 Jan 2022 18:32:40 No.14102743 Report

Quoted By: >>14102773

>>14102728
There are 3 children: Alice, Bob, and Charlie.
Alice and Bob are both ginger.
Bob and Charlie are both boys.
How many children are either ginger or boys?

Anonymous

Anonymous Fri 14 Jan 2022 18:32:52 No.14102745 Report

Quoted By: >>14103154

>>14102082
thats cool and all but it is meaningless because a 'set' is undefined. Could be a representation of infinity for all we know

Anonymous

Anonymous Fri 14 Jan 2022 18:34:45 No.14102756 Report

Quoted By: >>14102762

>>14102718
If x is any set, then {x} is a trivial group. Thus if X is the set of all trivial groups, then ?X is a set which contains all sets. In particular, ?X contains itself as its element.

Anonymous

Anonymous Fri 14 Jan 2022 18:36:15 No.14102762 Report

Quoted By: >>14102769

>>14102756
>If x is any set, then {x} is a trivial group
...under what operation?

Anonymous

Anonymous Fri 14 Jan 2022 18:38:47 No.14102769 Report

Quoted By:

>>14102762
x*x = x

Anonymous

Anonymous Fri 14 Jan 2022 18:38:59 No.14102773 Report

Quoted By: >>14102784

>>14102743
four, next question

Anonymous

Anonymous Fri 14 Jan 2022 18:41:56 No.14102784 Report

Quoted By:

>>14102773
So 4 out of 3 kids are either ginger or a boy?

Anonymous

Anonymous Fri 14 Jan 2022 18:46:35 No.14102802 Report

Quoted By:

>>14101949
I walked straight in, playing it Bogart, like I'd done a hundred times before.

Anonymous

Anonymous Fri 14 Jan 2022 18:51:20 No.14102835 Report

Quoted By:

>>14102732
Thank you!

Anonymous

Anonymous Fri 14 Jan 2022 20:06:31 No.14103154 Report

Quoted By:

>>14102745
it's not even a representation of infinity. it's literally meaningless.

Anonymous

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Anonymous Fri 14 Jan 2022 20:10:07 No.14103174 Report

Quoted By:

the fact that nobody has either
A) posted
B) complained about the lack of
a Fitch derivation in formal first-order logic of OP's claim from the ZFC axioms is...
you're never going to crack the math grading resources nut with an attitude like that

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