I feel like this is the kind of mistake people must have made before they had set theory

[sniffnoy]

...although admittedly, without set theory, it would be kind of hard to state this sort of thing in the first place.

Doing complex analysis homework; want to prove a certain set has measure <1/n. Which I am thinking of as "all points meeting this condition lie in a set of measure <1/n". So I take a point, suppose it's in the set, well then it must be in one of these sets of measure <1/n. So it's in a set of measure <1/n!

It wasn't until I actually rewrote it in more set-theoretic language that I noticed the sheer dumbness of that. By that logic - well, any point lies in a set of measure 0, you can draw the conclusion...

-Harry

Comments

[joshuazelinsky.livejournal.com]

The problem seems to not have anything to do with set theory but rath that English is not a great language for being clear on the order of your quantifiers.

[sniffnoy.livejournal.com]

Yeah, I guess that's a more accurate assessment...

[joshuazelinsky.livejournal.com]

Variants of this notation are from the late 19th century although the modern forms are I think from the early 20th (not sure of when the upside A and backwards E notation became prominent). The general go to source for notation is Cajori's (very dry) "A History of Mathematical Notations" but I don't remember him discussing quantifiers. (I haven't looked at the book in a very long time and I don't know where my copy is.) His book also stops at around 1900 so I suspect that my memory is accurate here.