From the VisualWorks Non-Commercial List

Given the following code:

set1 := Set with: 2 with: 3 with: 4.

set2 := Set with: 4 with: 3 with: 2.

Should:

set1 = set2 ?

BTW, the above in Smalltalk reads set1 is equal to set2.

The answer is that in VisualWorks it does not but in Squeak it does. I favor the Squeak implementation. In anycase, we also got a taste of Set theory. Check out my favorite line out of the thread:

“You are right on target. The so-called “axiom of regularity” in ZFC axiomatic set theory forbids self inclusion. This was needed to avoid Russell’s antinomy and a number of related paradoxes. Depending on the formulation of the set theory (there are so many!), you either get axioms of this form or the theory is constructive (the “type theory” solution of Russell and Whitehead), again forbidding self inclusion. I’m not aware of any modern set theories where the term “set” is used to denote a mathematical object which can contain itself.

I ain’t no mathemetition though…”

Gotta love that.

BTW, click on Bertrand above if interested in reading more about his “paradox”.