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A comment on Much less than, Much greater than symbols.

Re:Much less than, Much greater than symbols by kelnos on Sunday September 12, 2021 @01:14AM (#28498778)
This led me to learn:

    ⋘ U+22D8 VERY MUCH LESS-THAN
    ⋙ U+22D9 VERY MUCH GREATER-THAN
... which for some reason made me chuckle.
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Re:Much less than, Much greater than symbols by Izkata on Sunday September 12, 2021 @05:14AM (#28499673)
Got me curious so I just did a search for "less than" and found some more interesting ones:

≰ NEITHER LESS-THAN NOR EQUAL TO - https://www.fileformat.info/info/unicode/char/2270/index.htm

≨ LESS-THAN BUT NOT EQUAL TO - https://www.fileformat.info/info/unicode/char/2268/index.htm

⪒ GREATER-THAN ABOVE LESS-THAN ABOVE DOUBLE-LINE EQUAL - https://www.fileformat.info/info/unicode/char/2a92/index.htm

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Re:Much less than, Much greater than symbols by bruce343434 on Sunday September 12, 2021 @07:11AM (#28500097)
>LESS-THAN BUT NOT EQUAL TO

what's the point of this? This is already implied with just "<"

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Re:Much less than, Much greater than symbols by layer8 on Sunday September 12, 2021 @09:27AM (#28500936)
"<" is used to represent partial-order relations, and partial orders are often non-strict (i.e. really less-than-or-equal). Then LESS-THAN BUT NOT EQUAL TO can be used to denote that a particular pair is partially-ordered but not equal (i.e. strict partially ordered). In the same vein there’s also SUBSET OF WITH NOT EQUAL TO (U+228A).
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Re:Much less than, Much greater than symbols by bruce343434 on Sunday September 12, 2021 @10:55AM (#28501707)
I don't understand. "equal" and "less than" are disjoint. "subset" and "equals" are not disjoint (equal sets are each others subsets), so that's a whole different example.
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Re:Much less than, Much greater than symbols by layer8 on Sunday September 12, 2021 @11:14AM (#28501891)
In mathematics, the symbol "<" is also used for non-strict partial orders, where it effectively means “less than or equal to” instead of “strictly less than”. Working with non-strict partial orders is often easier than working with the equivalent strict partial order, and for economy of notation/ease of writing some mathematicians still use “<“ then instead of “≤”. In the rare cases they want to express strictly-less-than for a particular pair in the non-strict partial order, they can use the “less than but not equals” sign.

> "subset" and "equals" are not disjoint (equal sets are each others subsets)

There is “⊂” vs. “⊆” just like there’s “<“ vs. “≤”. A set is not a strict subset of itself, merely a non-strict subset of itself.

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Re:Much less than, Much greater than symbols by alexvoda on Monday September 13, 2021 @06:53AM (#28509872)
> and for economy of notation/ease of writing some mathematicians still use “<“ then instead of “≤”. In the rare cases they want to express strictly-less-than for a particular pair in the non-strict partial order, they can use the “less than but not equals” sign.

This is pure bullshit of the highest grade. Is is a perfect example of newspeak. "The symbols I use mean what I say they mean whenever I say so". It is gatekeeping. It is part of what makes math impenetrable for a lot of people. It is lazy. It is absurd. Such a lack of consistency is absurd for a rigorous field like math. It is a perfect example of my belief that mathematicians are abysmal linguists. I do not understand why mathematicians have this attitude towards their communication medium. If I could ask a genie for a wish, I would force the use of a compiler and a linter on all mathematicians. If your paper does not pass compilation and linting it gets automatically deleted. Bullshit!

/rant

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Re:Much less than, Much greater than symbols by bruce343434 on Sunday September 12, 2021 @01:00PM (#28502809)
Thanks, now I understand.
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Re:Much less than, Much greater than symbols by thih9 on Sunday September 12, 2021 @05:25AM (#28499728)
How is the ⪒ used?
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Re:Much less than, Much greater than symbols by this-pony on Sunday September 12, 2021 @06:10AM (#28499879)
I could see people using this symbol when proving for example that x = 0. Say they first show x \geq 0 and then x \leq 0. Then they've shown x ⪒ 0, and therefore x = 0. But yeah, a symbol like '⪒' for this purpose is maybe natural to write on a blackboard, maybe not so much in electronic form.

I'm not aware of any other purposes.

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Re:Much less than, Much greater than symbols by petters on Sunday September 12, 2021 @06:11AM (#28499886)
If a ≤ b or b ≤ a. That does not always have to be the case. For example, x ≤ y could mean that x is a descendant of y in a tree.
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Re:Much less than, Much greater than symbols by marcosdumay on Sunday September 12, 2021 @01:50PM (#28503225)
Interestingly, that last one seems to be missing from LaTeX.
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Re:Much less than, Much greater than symbols by afiori on Sunday September 12, 2021 @04:28AM (#28499486)
now I want the also the absurdist VERY MUCH LESS-THAN OR EQUAL
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Re:Much less than, Much greater than symbols by askvictor on Sunday September 12, 2021 @05:11AM (#28499659)
Would that be an implicit inclusive or (i.e. very much less than, much less than, less than, or equal), or exclusive (very much less than or equal, but not much less than or less than)?
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Re:Much less than, Much greater than symbols by HPsquared on Sunday September 12, 2021 @05:27AM (#28499736)
Exclusive, I reckon.
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Re:Much less than, Much greater than symbols by askvictor on Sunday September 12, 2021 @08:30PM (#28506560)
I want "much equal to", and "very much equal to". Which, in scientific terms, or floating point comparisons, would probably make some sense
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Re:Much less than, Much greater than symbols by drran on Sunday September 12, 2021 @05:19AM (#28499695) 

  0 ⋘===8
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Re:Much less than, Much greater than symbols by stavros on Sunday September 12, 2021 @04:50AM (#28499556)
Oh God yes
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Re:Much less than, Much greater than symbols by isoprophlex on Sunday September 12, 2021 @03:50AM (#28499350)
This triggers a doge meme in my mind... Wow, such very much less-than!
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Re:Much less than, Much greater than symbols by beerandt on Sunday September 12, 2021 @12:49PM (#28502716)
When you're trying to convince STEM professionals to go from hand written design documents to computer generated, you'd better be able to reproduce every little symbol that they're accustomed to using, or else it's just an excuse for non-compliance.

Something like:

(X+1)/X ≈ 1 for X ⋙ 1

We actually use a bit for showing derivation work on engineering design documents, especially for stating requirements for an equation to be valid. Or for equations that need to be simplified to be algebraically solved.

A one line equation might have two pages of definitions, assumptions, and constraints.

In this case, ⋙ is used to mean not just much greater-than, but big enough to justify whatever the simplification it is that you're making.

Eg, 10 could be considered much greater (≫) than 1, but is still a 10% error in the equation above.

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Re:Much less than, Much greater than symbols by iratewizard on Sunday September 12, 2021 @01:50AM (#28498893)
This is getting ridiculous. How long until we have things uncountably more than other things?
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Re:Much less than, Much greater than symbols by infogulch on Sunday September 12, 2021 @01:58AM (#28498930)
Could you combining-character an aleph-1 symbol on top of one of these?
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Re:Much less than, Much greater than symbols by thaumasiotes on Sunday September 12, 2021 @02:04AM (#28498951)
In math, when you care about the details of how small one thing is compared to some other thing, you probably use little-o notation. It's the same thing you're probably familiar with from computer science.

So if y is small compared to x, you might say y = o(x), or if it's really small compared to x, you might say y = o(x²), or if it's really really really small, o(x⁶)... whatever you need for your proof.

(o(x²) is more impressively small than o(x) because x < 1)

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Re:Much less than, Much greater than symbols by HPsquared on Sunday September 12, 2021 @05:31AM (#28499749)
Nice

That reminds me of something about the Greek letters Omega (Ω, ω) and Omicron (Ο, ο). O-mega means "big O" and O-micron means "small O".

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Re:Much less than, Much greater than symbols by emilsedgh on Sunday September 12, 2021 @03:55AM (#28499369)
Isn't that +∞ and -∞?
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Re:Much less than, Much greater than symbols by jimktrains2 on Sunday September 12, 2021 @08:55AM (#28500707)
Some infinities are countable.
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Re:Much less than, Much greater than symbols by marcosdumay on Sunday September 12, 2021 @01:52PM (#28503248)
Yes, but the GP's idea extends to larger infinities.
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Re:Much less than, Much greater than symbols by masklinn on Sunday September 12, 2021 @04:50AM (#28499558)
It seems closer to the aleph numbers.
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