# What's the problem with these alphabetic collisions?

I'm reading Halmos' Naive Set Theory.

According to the usual and natural convention "for some $y\,(x\, \epsilon \, A)$" just means "$x\, \epsilon \, A"$. It's equally harmless if the letter used has already been used with "for some-" or "for all-." Recall that "for some $x \, (x\, \epsilon \, A)$ means the same as "for some $y\, (y\, \epsilon \, A)$; it follows that a judicious change of notation will always avert alphabetic collisions.

It seems they change the letter to avoid these alphabetic collisions, but what's the problem with it? For me, it's clearer when it's stated without the letter chaging, just as in the bold text. Where are these alphabetic collisions going to be harmful? In the past, I felt confused when I saw "for some $y\,(x\, \epsilon \, A)$", I thought it was a statament about two objects.

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This doesn't make sense. Can you give more context? –  Ted Nov 21 '12 at 16:59
The $>$ is a typo. –  Andres Caicedo Nov 21 '12 at 17:00
do you mean to use the symbol $\in$? –  Holdsworth88 Nov 21 '12 at 17:02
@Holdsworth88: The $\in$ symbol is known as $\epsilon$-relation. In fact the original notation used $\epsilon$ and you can find old papers which used it that way. Halmos' book is quite old nowadays. –  Asaf Karagila Nov 21 '12 at 17:04
I believe I have corrected two typos in the quoted text. –  Arthur Fischer Nov 21 '12 at 17:17