Re: Atomic vs. atomistic
- From: Butch Malahide <fred.galvin@xxxxxxxxx>
- Date: Fri, 27 Nov 2009 00:48:17 -0800 (PST)
On Nov 26, 6:05 pm, Victor Porton <por...@xxxxxxxx> wrote:
On this Wikipedia page:http://en.wikipedia.org/wiki/Boolean_algebras_canonically_defined
is written:
"Such an algebra can be defined equivalently as a complete Boolean
algebra that is atomic, meaning that every element is a sup of some
set of atoms."
However in this Wikipedia page:http://en.wikipedia.org/wiki/Lattice_(order)
is written:
* Atomic if for every nonzero element x of L, there exists an atom a
of L such that a ≤ x ;
* Atomistic if every element of L is a supremum of atoms. That is, for
all a, b in L such that a\nleq b, there exists an atom x of L such
that x\leq a and x\nleq b.
Thus, accordingly the latter, the Boolean_algebras_canonically_defined
should speak about "atomistic" rather than about "atomic" lattices.
Where is the error? and what is the correct usage of terms?
Why do you think there is an error? Your first quotation speaks of
complete Boolean algebras. In the special case of complete Boolean
algebras, "atomic" is equivalent to "atomistic". So what?
.
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