5 ms·

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 differe

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.

layer8 5y ago
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.
- bruce343434 5y ago
  Thanks, now I understand.
- alexvoda 5y ago
  > 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

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.

layer8 5y ago

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.

bruce343434 5y ago
Thanks, now I understand.
alexvoda 5y ago
> 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