/sci/ - Science & Math » Thread #10313514

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Let's see how smart /sci/ is...

Anonymous Sun 20 Jan 23:50:19 2019 No.10313514 View Reply Original Report

Quoted By: >>10313519

Which of the following hold
$<br /> \forall x \in \emptyset \colon x = x \\<br /> \forall x \in \emptyset \colon x \not= x \\<br />$

Anonymous

Anonymous Sun 20 Jan 2019 23:52:51 No.10313519 Report

Quoted By: >>10314028

>>10313514
both

Anonymous

Anonymous Sun 20 Jan 2019 23:57:51 No.10313534 Report

Quoted By: >>10313672 >>10314028

any universal quantifier on the empty set is vacuously true

Anonymous

Anonymous Mon 21 Jan 2019 00:38:36 No.10313672 Report

Quoted By: >>10314028 >>10314440

>>10313534
This. Let's prove this and get this shit thread out of the way.
$\frac{\displaystyle \frac{\displaystyle \frac{\displaystyle \frac{\displaystyle \frac{\displaystyle \frac{\displaystyle \frac{}{B \;\vdash\; B} \quad{\rm (Ax)}}{B,\;\neg B \;\vdash\;} \quad{\rm (\neg L)}}{B,\;\neg B \;\vdash\; A} \quad{\rm (W R)}}{B\,\wedge\,\neg B \;\vdash\; A} \quad{\rm (\wedge L)}}{x\;\in\;\varnothing \;\vdash\; A} \quad{\rm (\varnothing L)}}{\vdash\; x\;\in\;\varnothing \;\Rightarrow\; A} \quad{\rm (\Rightarrow R)}}{\vdash\; \forall x,\; \left(x\;\in\;\varnothing \;\Rightarrow\; A\right)} \quad{\rm (\forall R)}$

Anonymous

Anonymous Mon 21 Jan 2019 03:49:35 No.10314028 Report

Quoted By: >>10314047 >>10314116

>>10313672
>>10313534
>>10313519
Sure, but why make a statement about elements of the empty set? You start talking about x element of (/) and I cut you off before you're done and say, "there is no element of the empty set, you dumbass." Now I'm right and you look like an idiot.

Anonymous

Anonymous Mon 21 Jan 2019 03:56:45 No.10314047 Report

Quoted By: >>10314087

>>10314028
you look like an idiot.

Anonymous

Anonymous Mon 21 Jan 2019 04:17:56 No.10314087 Report

Quoted By: >>10314097 >>10314110 >>10314209 >>10314486

>>10314047
No, I cut you off as you were saying the words, "element of the empty set." Idiot.

Anonymous

Anonymous Mon 21 Jan 2019 04:20:35 No.10314092 Report

Quoted By:

I hope you like dealing with special cases for universal quantifiers over a union of two sets.

Anonymous

Anonymous Mon 21 Jan 2019 04:24:14 No.10314097 Report

Quoted By: >>10314146

>>10314087
>"I'm better at math because I can interrupt you!"
The absolute state of /sci/

Anonymous

Anonymous Mon 21 Jan 2019 04:27:41 No.10314110 Report

Quoted By: >>10314146 >>10314155

>>10314087
>t. doesnt know material implication

Anonymous

Anonymous Mon 21 Jan 2019 04:30:11 No.10314116 Report

Quoted By: >>10314146

>>10314028
>there are no unicorns
>therefore every unicorn is purple
How is this confusing?

Anonymous

Anonymous Mon 21 Jan 2019 04:38:55 No.10314146 Report

Quoted By: >>10314155 >>10314157

>>10314097
>>10314110
>>10314116
>start a sentence with a false premise
You guys are just talking gibberish. Here's one for you, maybe you'll understand:
God does not exist, therefore Jesus is his son.

Anonymous

Anonymous Mon 21 Jan 2019 04:43:16 No.10314155 Report

Quoted By: >>10314159

>>10314146
see >>10314110

Anonymous

Anonymous Mon 21 Jan 2019 04:44:19 No.10314157 Report

Quoted By:

>>10314146
Okay, enjoy having special cases for empty sets whenever you talk about universal quantifiers over unions.

Anonymous

Anonymous Mon 21 Jan 2019 04:44:24 No.10314159 Report

Quoted By: >>10314187

>>10314155
>If it rains tomorrow, I will bring an umbrella
>It doesn't rain tomorrow
Who cares then?

Anonymous

Anonymous Mon 21 Jan 2019 04:55:11 No.10314184 Report

Quoted By:

If the Riemann hypothesis is false, (if the Riemann hypothesis is true, [the Eiffel Tower is in France]) is true.

Anonymous

Anonymous Mon 21 Jan 2019 04:57:18 No.10314187 Report

Quoted By: >>10314201

>>10314159
>Who cares then?
exactly you fucking idiot
we dont care, so the implication is still true if the premise isnt met
what the fuck do you not understand about this simple shit

Anonymous

Anonymous Mon 21 Jan 2019 05:03:50 No.10314201 Report

Quoted By: >>10314218 >>10314240

>>10314187
I understand buddy. But when has any of this ever been useful other than in the case: prove that every set contains the empty set.

Anonymous

Anonymous Mon 21 Jan 2019 05:06:31 No.10314209 Report

Quoted By: >>10314257

>>10314087
Wow, an actual retard.

Anonymous

Anonymous Mon 21 Jan 2019 05:08:04 No.10314218 Report

Quoted By: >>10314257

>>10314201
Moron. "Every set contains the empty set" is false.

Anonymous

Anonymous Mon 21 Jan 2019 05:13:16 No.10314240 Report

Quoted By: >>10314257

>>10314201
>But when has any of this ever been useful
in proofs you fucking ass hat

if you have a set A
and the elements of A satisfy P and not P
then A is empty
and youve all of a sudden learned an awful lot about P in the process

youre just exposing the fact that you dont have experience with math

Anonymous

Anonymous Mon 21 Jan 2019 05:17:02 No.10314257 Report

Quoted By: >>10314263 >>10314267 >>10314486

>>10314218
>assume there exists an x element of the empty set not element of some other set
>then there exists an element of the empty set
>this is a contradiction. Thus, every set contains the empty set.
>>10314209
>>10314240
>I have a bachelor's in math from a top tier university

Anonymous

Anonymous Mon 21 Jan 2019 05:18:59 No.10314263 Report

Quoted By: >>10314275

>>10314257
Psst, I think the concept you're looking for is "subset".

Anonymous

Anonymous Mon 21 Jan 2019 05:20:20 No.10314267 Report

Quoted By: >>10314287

>>10314257
ffs
read a book

Anonymous

Anonymous Mon 21 Jan 2019 05:22:28 No.10314275 Report

Quoted By: >>10314281

>>10314263
>subset and containment are different concepts

Anonymous

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Anonymous Mon 21 Jan 2019 05:23:41 No.10314281 Report

Quoted By: >>10314297

>>10314275

Anonymous

Anonymous Mon 21 Jan 2019 05:25:09 No.10314287 Report

Quoted By: >>10314309

>>10314267
I bet you haven't read all of Rudin's 3rd edition of analysis.

Anonymous

Anonymous Mon 21 Jan 2019 05:26:56 No.10314297 Report

Quoted By: >>10314302 >>10314309

>>10314281
>masters in financial engineering from a top tier uni
I'm actually a lot smarter than you.

Anonymous

Anonymous Mon 21 Jan 2019 05:27:54 No.10314302 Report

Quoted By: >>10314325

>>10314297
>dick measuring contest

Anonymous

Anonymous Mon 21 Jan 2019 05:31:05 No.10314309 Report

Quoted By: >>10314325

>>10314297
>masters
>doesnt understand sets 101
>or even implication
nice proof of the worthlessness of that degree

>>10314287
havent read it all yet, anal is easy tho and rudin is readable despite being dense

Anonymous

Anonymous Mon 21 Jan 2019 05:36:57 No.10314325 Report

Quoted By: >>10314331 >>10314332

>>10314302
>implying my dick size isn't all that matters in life
>>10314309
If A is a subset of B then A is contained in B. Pretty simple right?

Anonymous

Anonymous Mon 21 Jan 2019 05:39:09 No.10314331 Report

Quoted By: >>10314363

>>10314325
>Pretty simple right?
thats literally fucking wrong
if A is a subset of B
then the elements of A are contained in B
you dont know what youre talking about
keep it to finance next time dipshit

If you have the set of Natural numbers,
then the set of the even Naturals is a subset
but the set of the Naturals, ONLY contains numbers
it doesnt contain sets, right? right.

Anonymous

Anonymous Mon 21 Jan 2019 05:39:09 No.10314332 Report

Quoted By:

>>10314325
"Contained" is ambiguous terminology. The other anon may be interpreting containment as membership.

Anonymous

Anonymous Mon 21 Jan 2019 05:51:48 No.10314363 Report

Quoted By: >>10314386 >>10314437 >>10314891

>>10314331
>keep it to finance
I'm literally required to pass real and complex analysis for my degree
>the set of Naturals only contains numbers
>it doesn't contain sets
no. Sets contain sets. The set of naturals contains sets of naturals. Numbers like 1, 2, etc. are elements of the set of naturals. The set of naturals contains sets such as 2N, 3N, 2N+1, the set of numbers divisible by 3 but not 2, the set of primes, {1,2,3}, etc.

Anonymous

Anonymous Mon 21 Jan 2019 06:00:44 No.10314386 Report

Quoted By: >>10314402

>>10314363
sets contain their elements
the power set of a set contains the subsets of the original set

Anonymous

Anonymous Mon 21 Jan 2019 06:06:53 No.10314402 Report

Quoted By:

>>10314386
>a subset is an element
dumbass

Anonymous

Anonymous Mon 21 Jan 2019 06:23:47 No.10314437 Report

Quoted By: >>10314484

>>10314363
>Sets contain sets.
How stupid do you have to be, to think that saying “the empty set contains the empty set” sounds reasonable
Its fucking empty, it shouldnt contain anything
A set of numbers should contain numbers, not sets.
Using containment to refer to subsets is patently retarded

Anonymous

Anonymous Mon 21 Jan 2019 06:25:18 No.10314440 Report

Quoted By:

>>10313672
this looks really gay, I just want you to know weird alien symbols appeared when i clicked on the TeX. Did you use the inhouse TeX converter or did you copy paste that? Trying to gauge how tired and possibly mad i am

Anonymous

Anonymous Mon 21 Jan 2019 06:48:14 No.10314484 Report

Quoted By:

>>10314437
All sets contain themselves. Therefore, the empty set is a subset of itself.
https://math.stackexchange.com/questions/334666/is-the-empty-set-a-subset-of-itself

Anonymous

Anonymous Mon 21 Jan 2019 06:49:08 No.10314486 Report

Quoted By:

>>10314087
Then you won't know what the statement is. Don't question the if-part of the assumption, just pretend it's true and if it leads to a contradiction use the contradiction to finish the proof as in >>10314257

Anonymous

Anonymous Mon 21 Jan 2019 08:12:15 No.10314588 Report

Quoted By:

>this thread
the absolute state of /sci/

Anonymous

Anonymous Mon 21 Jan 2019 12:21:12 No.10314891 Report

Quoted By: >>10314901

>>10314363
>Numbers like 1, 2, etc. are elements of the set of naturals
It's sets all the way down, buddy.

Anonymous

Anonymous Mon 21 Jan 2019 12:25:54 No.10314901 Report

Quoted By:

>>10314891
So 1 ={1}? Heh, I don't think so.

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