/sci/ - Science & Math

[Anonymous No.8978828]

Discuss.

[Anonymous No.8978830]

>>8978828
could someone post a proof where it's nessecary to know something is a specifically a proper subset, aside from something trivial like "prove that this subset I just thought of is a proper subset"?

[Anonymous No.8978836]

>>8978828
P = NP

We know P is subset of NP. Is it proper subset? Answer will net you $6 gorillion.

[Anonymous No.8978842]

>>8978828
(1) is the only acceptable choice.

[Anonymous No.8978848]

>>8978842
This.

[Anonymous No.8978861]

>>8978828
The first one is obviously the best but for the sake of clarity I'd use the third one.

[Anonymous No.8978882]

>>8978861
3 is redundant. 1 is good.

[Anonymous No.8978886]

>>8978828
>>8978842
>>8978848
>>8978861
>>8978882
They're all fine, as long as it's consistent
I always use the first as it's most common but I do not care what a textbook or paper uses

[Anonymous No.8979052]

2 is the only answer. One rarely works with proper subsets so it's faster to write [math]\subset[/math] and add these strokes when you need to emphasize the subset is proper

[Anonymous No.8979061]

If you use the ⊂ symbol to mean ⊆ , go fuck your self.

[Anonymous No.8979078]

>distinguishing between proper and improper subsets
>not using set builder notation to denote subsets

I didn't know /sci/ was this uncivilized

[Anonymous No.8979094]

>>8979052
2 us the only wrong answer, but it's indeed faster and everybody can understand you. But that's not a mathematical argument.

[Anonymous No.8979148]

>>8978828
2

use the simple symbol for "subset"
A\neq B is an added special condition, and should be marked like a diacritic; 1 is annoying bc it does the reverse (really, writing a special diacritic every time to indicate the usual meaning?); 3 is annoying bc you have to write something extra for every instance

[Anonymous No.8979152]

>>8979061
>>8979052

sorry buds but you'll have to grow up eventually. 2 is probably the most common in books I've seen on topics that use it a ton like topology

[Anonymous No.8979311]

>using set theoretic terminology
HAHAHAHAHHAHAHAHAHHAHAHAHAHAHAHHAHAHAHAHAHHAHAHAHAHAHAHAHAHHAHAHA

[Anonymous No.8979327]

>>8978828
1 is correct
2 is absolute garbage
3 is also okay

[Anonymous No.8979329]

2 uses an additional line and 3 uses two additional lines

1 is best. Get over it, assumed old man reading this post.

[Anonymous No.8979335]

>>8979152
Ok dude, then go write "<" to to denote "≤". and when you want to denote "<", write "≤" with its bottom part strikethroughed.

[Anonymous No.8980281]

>>8978828

As most people have correctly said in this post, 1 is the best convention. One of my reasons for supporting this popular conclusion is that the convention in 1 is directly analogous to the now-standard notation for inequalities, and both senses semantically dovetail nicely with the distinct yet related senses of equality, both in the sense of equating quantities (numbers) and sets - the lower horizontal bar suggests the semantic /possibility/ of equality, though such is not necessarily required.

Consider these three lines by way of comparison:

[math]

1 < 2 \;\;\; ; \;\;\; 1 \leq 2 \;\;\; ; \;\;\; 2 \leq 2 \;\;\; ; \;\;\; 3 \nleq 2 \\

A = \{4\} \;\;\; ; \;\;\; B = \{4,7\} \;\;\; ; \;\;\; C = \{4,7,8\} \\

A \subset B \;\;\; ; \;\;\; A \subseteq B \;\;\; ; \;\;\; B \subseteq B \;\;\; ; \;\;\; C \not\subseteq B

[/math]

Furthermore, as you are aware, elementary relations tend to indicate /propositions/, statements which are capable in principle of being judged either true or false. And the /negation/ of such propositions is commonly accomplished via a strikethrough sign which goes through the /whole relation glyph/. The point being that such strikethroughs are common in this discourse, and that if you have two "strikethroughs" in a given glyph, it first of all looks ugly, and second of all creates /semantic confusion. Let me know what you think of the expression/proposition

[math] B \not\subsetneq B [/math]

[Anonymous No.8980301]

>>8978828
1. is the right way
3. is ok if you use a lot of crossed out symbols otherwise
kill yourself if you use 2

[Anonymous No.8980303]

>>8980281
> Let me know what you think of the expression/proposition B⊊̸B
You mean [math]B \supseteq B[/math] ?

[Anonymous No.8980316]

1 is the best if everyone could just agree on it
3 is the most explicit and I don't mind it

2 is pretty bad, yet it seems to be what I always encounter in books, so fuck everything

[Anonymous No.8980337]

ITT: undergrads

>>8979152
>>8979152
this guy is right and you would know this if you have read something other than a calculus textbook

[Anonymous No.8980364]

Every textbook past elementary school uses 2, so I'd rather stick to notation used by actual mathematicians and not listen to uneducated autists on sci

[Anonymous No.8980497]

I only use the symbol [math]\subset[/math]. If I want to say that [math]A\subset B[/math] and [math]A\neq B[/math], then I would write precisely the latter.

[Anonymous No.8980857]

>>8980364

This is a discouraging thought as 2 is clearly the worst of the three conventions on its face, even and especially in the case that what you say is true.

Your next instinct will be to ad hom about the quality of my education, but for the record I did complete a bachelor's, and my library as far as it goes (up to where the graduate level begins) never uses the glyph exclusive to 2 and 3. Nor did any of my professors, and several of them had been active since the 1980s.

I wonder if it's really more a question of European vs. American notation a la interval notation: [0,1) ; [0,1[ .

[Anonymous No.8980863]

>>8980364
That's not true. Only a few autistic writers do it. Most of them use 1 or 3.

[Anonymous No.8980883]

>>8980863
this guy uses 2

[Anonymous No.8981296]

{{{Set theory}}} notation in general is utter garbage. Take a look at this horror:
[eqn]A \,\setminus\, B \qquad\text{or sometimes even}\qquad A \,-\, B[/eqn]
[eqn]A \,+\, B \,=\, \left\{x \,+\, y \,:\, x \,\in\, A \,\wedge\, y \,\in\, B\right\} \qquad\text{but}\qquad A \,\times\, B \,=\, \left\{\left( x,\, y \right) \,:\, x \,\in\, A \,\wedge\, y \,\in\, B\right\}[/eqn]
Same thing for (((ring theory))):
[eqn]A^* \,=\, \left\{ x \,\in\, A \,\mid\, \exists y \,\in\, A,\, x\,y \,=\, 1_A \right\} \qquad\text{but}\qquad \mathbf Z^* \,=\, \mathbf Z \,\setminus\, \left\{ 0 \right\}[/eqn]

[Anonymous No.8982103]

>>8981296
butthurd engineer who can't understand mathematical notation
brevity over clarity, it's better to have small set of symbols and determine the meaning from the contest than have shitload of symbols nobody is able to remember

[Anonymous No.8982123]

>>8982103
>it's better to have small set of symbols and determine the meaning from the contest than have shitload of symbols nobody is able to remember
Then, I can beat 100% of mathematicians using only these:
[eqn]\vee\qquad \wedge\qquad \neg\qquad \forall\qquad \exists\qquad \Rightarrow\qquad \Leftrightarrow\qquad \in\qquad \left[ A,\, \ldots,\, Z,\, a,\, \ldots,\, z \right][/eqn]

[Anonymous No.8982552]

3 is the best. While I appreciate 1, 3 leaves no ambiguity. It may be uglier and require more strokes of the pen, but clarity is essential

[Anonymous No.8982663]

>>8978830
Not the example you wanted, but often when a book uses ⊂ to denote subset, and not proper subset, I get confused when I see it in a definition or proof, because I think the author means proper subset, when such a restriction wouldn't make sense in the given context.
To answer OP's question, I prefer 1, but I guess I'd be okay with 3 too.

[Anonymous No.8982667]

>>8979052
That's not a good reason to use it in a book though.

[Anonymous No.8982672]

>>8982123
(A⇔B) := (A⇒B)∧(B⇒A)

and if you're a classical logic shill
A∨B := ¬(¬A∧¬B)
∃x.A := ¬(∀x.¬A)

[Anonymous No.8982678]

>>8979152
>>8980337
>I want to feel like a big boy, so I adapt the arbitrary notational conventions I see in books written by big name mathematicians
You fags are no better than the idiots on /g/ who want to feel superior about the way their indent their code, so they bring up K&R.

[Anonymous No.8982727]

3 seems like the best to me purely because it's the only one with absolutely no ambiguity. However personally I use 2 because that's what all the lecturers on my course used.

[Anonymous No.8982969]

>>8980857
i am from germany and i see both. at my uni [0,1) seems to be dominant

[Anonymous No.8983159]

One of my lecturers used (and noted in his notes) that he will use 3, and use [math]\subset[/math] if there is no ambiguity that the sets are obviously not equal, as in you would write:
[eqn]\mathbb{N}\subset\mathbb{Z}\subset\mathbb{Q}\subset\mathbb{R}\subset\mathbb{C}[/eqn]
But not say:
[eqn]\{x:x \;\mathrm{a\;zero\;of\;the\;Riemann\;Zeta\;function\;on\;the\;line}\;\Re(x)=1/{2}\}\subset\{x: x \;\mathrm{a\; nontrivial\; zero\; of\; the\; Riemann\; Zeta\; function}\}[/eqn]