/sci/ - Science & Math

>>10313514
both

any universal quantifier on the empty set is vacuously true

>>10313534
This. Let's prove this and get this shit thread out of the way.
[eqn]\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)}[/eqn]

>>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.

>>10314028
you look like an idiot.

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

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

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

>>10314087
>t. doesnt know material implication

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

>>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.

>>10314146
see >>10314110

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

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

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

>>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

>>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.

>>10314087
Wow, an actual retard.

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

>>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

>>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

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

>>10314257
ffs
read a book

>>10314263
>subset and containment are different concepts

>>10314275

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

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

>>10314297
>dick measuring contest

>>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

>>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?

>>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.

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

>>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.

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

>>10314386
>a subset is an element
dumbass

>>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

>>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

>>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

>>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

>this thread
the absolute state of /sci/

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

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