Upside-down A's and Sideways E's

Date: 09/19/2001 at 17:23:14
From: Chang
Subject: Upside-down A's and Sideways E's

What is an upside-down A? a sideways E? Also, what do R and J stand 
for?

Date: 09/20/2001 at 08:48:57
From: Doctor Wolfson
Subject: Re: Upside-down A's and Sideways E's

Hi Chang,

These are called "quantifiers" and are used in a field called 
"propositional logic." A is called the Universal Quantifer, meaning 
that all members of one group are members of another group. You would 
read this as, "For All x, it is the case that..."

E is called the Existential Quantifier, and means that at least one 
member of the first group is in the second. If you see the E with a 
"!" after it, that means "exactly one." You would read the E statement 
as, "There Exists an x such that..."

For instance, if I wanted to say that all beagles are dogs, I can 
assign B(x) to the statement "x is a beagle" and D(x) to the statement 
"x is a dog", and say:

  Ax: B(x) -> D(x)

This means that for all things "x," it is true that if x is a beagle, 
then x is a dog.

I don't know of any universal meaning of R and J in this context, 
perhaps they are being used as variables, like my B and D.

I hope this helps. Feel free to write back if you'd like further 
clarification.

- Doctor Wolfson, The Math Forum
  http://mathforum.org/dr.math/