# Which came first, the $\exists$ or the $\forall$?

1. Jul 27, 2013

### 1MileCrash

I've always imagined that some mathematician or logician was looking for a cool way to write these quantifiers, and one of the following scenarios happened:

1.)

"Hey, I know, for "For All," I'll just take the letter "A" and flip it vertically, giving me this lovely $\forall$. Then I'll just do the same thing with the letter "E" for "There Exists."

But wait, the letter "E" is vertically symmetric, it'll look the same!" *flips it horizontally instead.

2.)

"Hey, I know, for "There Exists," I'll just take the letter "E" and flip it horizontally, giving me this lovely $\exists$. Then I'll just do the same thing with the letter "A" for "For All."

But wait, the letter "A" is horizontally symmetric, it'll look the same!" *flips it vertically instead.

So the question is, what came first, the $\forall$ or the $\exists$?

2. Jul 27, 2013

### micromass

Staff Emeritus
From wiki:

http://en.wikipedia.org/wiki/Quantification

3. Jul 27, 2013

### 1MileCrash

Another mystery dispelled by wikipedia.

4. Jul 27, 2013

### AlephZero

True but probably irrelevant. Both symbols are rotated through 180 degrees.

Before computer typesetting, using metal type "upside down" was an easy way to get new symbols.