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1. what does it mean? I know most of the other ones.

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2. (Original post by cooldudeman)
what does it mean? I know most of the other ones.

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I believe is the mathematical shorthand for "subset".

The same goes for being the shorthand for "not a subset".

Then again, it may be something completely different.
3. (Original post by cooldudeman)
what does it mean? I know most of the other ones.

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A curve opened right, the top of the (curved) arrow is on the left
4. (Original post by Khallil)
I believe is the mathematical shorthand for "subset".

The same goes for being the shorthand for "not a subset".

Then again, it may be something completely different.
I'm sure the subset one is this.

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5. (Original post by cooldudeman)
I'm sure the subset one is this.

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I'm pretty sure that those can be used interchangeably. I've seen various books in which this is the case.
6. (Original post by cooldudeman)
what does it mean? I know most of the other ones.

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"is a proper subset of" i.e. is contained in, but is not the whole thing (the one with the line underneath allows equality; it's like the distinction beyween < and <=)
7. (Original post by davros)
"is a proper subset of" i.e. is contained in, but is not the whole thing (the one with the line underneath allows equality; it's like the distinction beyween < and <=)
I don't think "is a proper subset of" is standard notation, although it is sometimes used like that.

The standard latex symbol for a proper subset is \subsetneq .
8. (Original post by DFranklin)
I don't think "is a proper subset of" is standard notation, although it is sometimes used like that.

The standard latex symbol for a proper subset is \subsetneq .
really? I'm sure we used to have 2 symbols available to make the distinction, but perhaps I'm misremembering

Edit: I've just grabbed a book at random from my cupboard - Kevin Houston's "How to Think Like a Mathematician" - and I'm not imagining things: his notation guide shows the symbol with the bar under it to mean "is a subset of", and the one without a bar under it to mean "is a subset of (but is not equal to)".
9. A not so random book:

Naive Set Theory by Paul Halmos:

To show that we show and

No lines.

Usage varies, and what's in favour may evolve with time and depend on what material is being presented, where they were taught, etc., which is why mathematicians must define their terms/symbols.
10. (Original post by ghostwalker)
A not so random book:

Naive Set Theory by Paul Halmos:

To show that we show and

No lines.

Usage varies, and what's in favour may evolve with time and depend on what material is being presented, where they were taught, etc., which is why mathematicians must define their terms/symbols.
Yeah - I've found an analysis book that confirms my memory but offers DFranklin's suggestion as an alternative; also Stewart & Tall's "Foundations" gives them the other way round!

Always best to check what convention your lecturer is using in these circumstances
11. I'm really confused because they specifically said the one with the line is the subset one. they never mentioned the one without the line.

if IN is written alone, what does it mean?

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12. It is sometimes used for proper subset, and sometimes for subset. I'd say the latter is probably more common, and it's rarely used where the distinction is important and non-obvious.
13. (Original post by davros)
really? I'm sure we used to have 2 symbols available to make the distinction, but perhaps I'm misremembering
To be clear, I meant it's not used universally enough to be considered a standard, rather than odd enough to be considered unusual or wrong.

My personal preference is always for non-ambiguity even if it requires slightly more writing, and so I would use \subseteq () and \subsetneq ()

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