Discuss

Discuss.

this is a troll right?

> is guilty of shit tier
proper subsets suck

Bait.

The shit tier is the correct one. We almost never care about proper subsets, so the extra line for subset is redundant.

From an information-theoretic standpoint, if we regard each stroke of the pen as a symbol, the "shit tier" is of the greatest entropy given the state of mathematical literature.

This is proof that the right column is ideal.

Yes.

im bad tier. I can't justify it because I've never thought about it enough to to have an opinion on the right way to do it because I'm not autistic

"Shit tier" is the best one.
Stay mad cuckboy.

>consistent notation is bait

>muh patterns

those two symbols are notations for entirely different relations between entirely different objects.

>entirely different
t. brainlet

>[math]\textrm{B}\subseteq\textrm{C}[/math] is the same thing as [math]\textrm{x}\leq\textrm{y}[/math] and [math]\textrm{B}\subset\textrm{C}[/math] is the same thing as [math]\textrm{x}

[math]B \subseteq C \Rightarrow |B| \leq |C|[/math]
[math]B \subset C \Rightarrow |B| < |C|[/math]
(for finite sets)

Yes. It's the Veeky Forums equivalent of /g/'s GNU vs. K&R vs. Allman indentation style etc. Just report and hide.

B={1,2,3,4}
C={0,1,2}

C is not a subset of B, but it's cardinality is lower. That notation would imply that any set with less elements than another would be a subset.

They're one-sided implications tho.

What?

doesn't surprise to see that brainlets using ⊂ for anything but proper subsets have such a shaky grasp on logic too

Yeah can you just explain what you meant by one sided implication?

I think the reason some use the shit-tier notation is that they don't work with proper subsets much, so they use the simple notation for the stuff they use the most.

[math] \Rightarrow [/math] reads as if
[math] \Leftrightarrow [/math] reads as if and only if
the first one is the one sided implication (the left implies the right)
the second is used if the two statements are equivalent (the left implies the right and the right implies the left)

Yeah, they're also the type of lazy idiots that define [math]\mathbb{N} = \mathbb{Z}^+[/math].

> define
doesn't matter which set is most of the time, just has to be an inductive and/or Archimedean set.

>can you just explain what you meant by one sided implication?
Jesus fuck, not even him but don't give your opinion in a math thread anymore.

You can use whatever you want but there is no universally accepted convention.

Is it not?

"shit tier" one is best but we should then also replace

kys

(You)

Mathematician
God Tier

You right

This is the worst part. Imagine studying something like analysis when you can never be sure if > means > or ≥

>⇒ reads as if
I am pretty sure that's 'only if'

>being an autist about notation

it just gets in the way of actual math

Bad notation does, that's right.

except all three categories communicate what they intend to, so it literally does not matter whatsoever.

And by mixing different notational conventions and letting everyone use their own retarded symbols, the actual math is delayed by confusion and the need for clarification on which is which.

if someone writes a paper where that distinction isn't clearly by the verbiage and they rely on symbols, then they're just a shitty writer. do you know nothing about good writing practice?

Its really not that confusing. Any book that uses the symbol that looks like a proper subset will never tell you, that when he uses it, it means proper subset. He will define A c B means all x in A then x in B, surely the other direction could hold, but its not necessary. If you need help understanding this stuff I suggest your professors office hours.

Define actual math

stuff people who aren't undergrads do

[math]\mathbf{N}[/math] is the set of non-negative integers, you absolute brainlet.

>[math]\mathbf{N}[/math] instead of [math]\mathbb{N}[/math]

A ⇒ B
in logic means
if A, then B

for example, take the statement
"if it is raining, then the ground is wet"
the A in this statement is "is raining", and B is "the ground is wet"
so we write A⇒B
but now think about what happens when you pour water on the ground
the ground is wet, but it's not raining, so A is false, but B is true

this is logical one-sided implication (the "one-sided" is usually omitted because MOST people know what "implies" means)

yup. my bad

I have a math degree and I sometimes look up math articles to amuse myself. And I post here, too, in the course of self-teaching the math that I didn't get in school in my spare time.

I don't recall ever seeing the notation at center and center-right at any point in my life.

Shit-tier, quite the opposite of being the best, is clearly shit from a semiotic-design point of view, and so it is worth telling these posters that they are simply wrong. That little tick mark is slightly hard to do properly, and is suggestive of negation. What is the negation that it is supposed to be suggestive of? /The negation of the possibility of equality of the two sets, which is exactly the semiotic meaning of the lower vertical bar/. As in, the lower bar of an equals = sign.

This is why the "God tier" convention is in actual fact the best piece of design. In addition to being (more or less) what I anecdotally was taught, this convention's semiotic design /marries up nicely with our well-established mutual understanding of the symbols of inequality/.

Although true that the matter doesn't come up much, it does come up. And when it does (and since it does), it makes sense to have a semiotically consistent convention in place. The top left symbol for "subset" holds open the possibility that the two sets in the relation may in fact be equal, just as the two inequality symbols >=,

subset/leq are partial orders and strict subset/lt are the corresponding linear orders man