Comparing Two Simple Sets: Differentiating with Consistent Logic

[Loren Booda]

Given a set of one element, and a set of two elements each like that of the first, is it possible to differentiate between the two sets using consistent logic to describe both the sets and their differentiation?

 

[Hurkyl]

{a} = {b, c} if and only if a = b and a = c.


You could talk about a different kind of thing: a multiset, for which [a] and [a,a] are different. (But, [a,b] and [b,a] are the same) But a multiset is generally not a set.

If you further want (a,b) and (b,a) to be different, you want to speak about ordered lists.

 

[Loren Booda]

Hurkyl,

I was surmising that the concept of unity or duality itself is "incompatible" with the actual transformation from unity to duality. Perhaps this idea is too philosophical for the Mathematics forum?

 

[Hurkyl]

*shrug* It all depends on if you can ask your question in a mathematical form. You can't really apply any sort of deductive logic to your question unless you first provide some premises from which one can argue. (e.g. what sort of properties shall we assume "unity" has? And what exactly is a transformation from "unity" to "duality", and which one are you talking about?)