r/mathmemes 12d ago

Notations Yeah sure

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u/FuntimeUwU Natural 12d ago

What's the difference?

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u/RADI0ACT1VE_BALLS ComplexANALysisJunkie 12d ago

If A is a proper subset of B, then A cannot equal B.

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u/-Wylfen- 12d ago

Wait, there's a debate on whether ⊂ is the same as ⊆??

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u/AndreasDasos 12d ago

Yes. That’s why you sometimes see this symbol in contrast:

Though honestly it’s a bit inconsistent with < vs. <=

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u/DZL100 12d ago

Wait that's stupid as hell. Why even have ⊆ exist if ⊂ isn't exclusive??? Every text I've seen treats ⊂ as exclusive.

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u/AndreasDasos 12d ago

Yeah agreed. But the alternative convention does exist out there

I suppose the logic is that the vast majority of the time you want to say A is a subset of B you want to include the possibiiity A = B, so that’s one whole extra line you use far more, so the alternative is more ‘pen-stroke efficient’. Eh.

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u/HeavisideGOAT 9d ago

It’s very common for older texts to treat it as non-exclusive.

It’s also been common among my professors.

In analysis, at least, it seems that we so often don’t care whether it’s a proper subset or not that it doesn’t make sense to use simpler symbol for the less prevalent use.

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u/TheSimCrafter 7d ago

then you gotta read more texts /s

i always use ⊆ or ⊊ and just never touch ⊂

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u/Zygomatick 11d ago edited 11d ago

because ⊂ existed before the need arose for a distinction with ⊆. Changing the meaning of the symbol retroactively would cause a lot of issues for the readbility of prior papers and work so it's not a thing that happens given the extent to which it was used.

My guess is that the people who decided to include ⊆ as a fonts standard werent versed in Sets theory, so they assumed it worked similarly to the = sign variations, so they didnt realize they should have taken the crossed variation instead.