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/
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